Encumbrance is probably the single most hated and ignored rule in all of Dungeons & Dragons history (although 'keeping track of literally every material spell component' gives Encumbrance a run for its money). I've never met a player who enjoyed all the bookkeeping necessary to ensure encumbrance compliance, although I have met my fair share of DMs who take obscene delight in hosing the party on weight restrictions at critical moments. Encumbrance is the gaming equivalent of diagramming sentences in your English class: it does little more than waste time which could be spent doing literally anything else for a greater reward.
That said, as a Dungeon Master myself, while I hate Encumbrance, I am a huge fan of the, "You didn't buy it? Then you don't have it!" club. This isn't (solely) because I want to be a dick to my players, it's because I want to spur them on to greater heights of creativity than even they thought possible. See also: schadenfreude. Some of my most memorable times around the gaming table have involved my PCs using seemingly unrelated mundane items to MacGyver their way out of difficult situations. With a little planning and some creativity, you can turn nearly anything in the Player's Handbook into a way out of a potential problem, so let's take a look at the basic Adventuring Gear table from page 150 and suss out some not-so-obvious uses for some not-so-obvious equipment.
The abacus may be associated with commerce, and if you fancy yourself a wandering merchant or travelling trader you'll definitely want to spare the 2 gold pieces necessary to add one to your pack. But what if all you care about is hitting things with a sword? Is an abacus really necessary? My answer is an unequivocal 'YES!', especially if you're playing a character with a low Intelligence score. An abacus in D&D is the equivalent of a pocket calculator app for your smartphone. While characters of average or higher intelligence can probably do simple arithmetic in their heads (or at least with parchment and a quill), low-intelligence characters are at the whim of others to be honest in their trade dealings. An abacus levels that playing field, and all but the most grotesquely ignorant buffoon can be taught how to use one to avoid getting cheated in tasks requiring basic math.
An abacus could also be broken in a pinch, with the colorful beads used to distract or trade with low-intelligence foes, thrown to create distractions, or used in conjunction with illusion magic to give the impression of handing something physical to someone else. Other items can accomplish this more cheaply, but we're talking about an emergency backup plan here, not a go-to first step.
At 25 gold pieces per vial, acid won't be first on the shopping list of most low-level adventurers. Its write-up in the PHB explains it in terms of weaponized use, allowing the wielder to splash it on nearby foes or hurl it at targets up to 20 feet away, to cause an instant 2d6 acid damage. Given enough of a supply, you could conceivably use it to melt a Tarrasque.
But the vial of acid is actually more useful outside of combat. Acid wrecks other substances, including metal, which means that you could use it to eat through a stubborn lock, dissolve incriminating evidence, etch a symbol or words into stone, and so on. Sneaky types could rig up drop traps with acid to protect a doorway, or in conjunction with an alarm bell. Those trending toward the evil spectrum of Alignment are already thinking about its possibilities for information extraction and enhanced interrogation (ie: torture). Finally, acid prevents Trolls from regenerating, meaning you can use it to kill one once you've got it down to zero hit points--in fact, any PC who can't cast Acid Splash or Firebolt should carry at least one vial of acid on them at all times for just this purpose.
Alchemist's Fire is basically medieval napalm: it ignites on contact with air, sticks to whatever it touches, and burns for...well, the PHB doesn't actually say how long it will burn, but unlike an acid splash, it lasts for longer than one round. The book is only concerned with its combat application, but like the acid vial it can also be used to kill a Troll (although at 50 gold per flask, it's even less economical than acid for this job).
Outside of setting something on fire for 1d4 damage until it dies or succeeds on a DC 10 Dexterity check to extinguish the flames, Alchemist's Fire is invaluable for when you absolutely, positively need to light something ablaze. As a DM, I'd rule it works much the same as the Create Bonfire cantrip: smashed on a surface, it spreads across a 5'-by-5' area, burns for five minutes (fifty rounds), and sets fire to anyone or anything that moves into or through the area. Budding arsonists are already thinking about uses for this fantasy Molotov cocktail. If you're transporting flasks of Alchemist's Fire, make sure they are secured in a reinforced, padded container. Otherwise you risk a re-enactment of that scene from Saving Private Ryan...
Pretty much what it says on the tin. Aside from giving the drinker advantage on poison-related saving throws for an hour, there's not much else you can do with this 50 gp bottle of liquid. Not everything needs a creative use.
Quintessential adventuring gear, the backpack is used solely for hauling stuff without taking up one or both hands. At two gold pieces, it's too expensive for alternate uses when there are much cheaper options, but this is one of those "everybody needs one" items that ensures you can lug around gear you don't need instant access to. Savvy adventurers will reinforce the bottom of the pack with wood or metal to keep thieves from cutting out the bottom though, so talk to your DM about this before you stroll through the areas of town where criminals are known to congregate.
According to the PHB, a single backpack can hold 30 pounds of gear, but they also have areas for strapping a bedroll and coil of rope to their exteriors, which is nice, so don't forget that.
For one gold piece, you get 1,000 small, round pieces of metal that you can scatter across a a 10'x10' square to create dangerous terrain. This is great for battlefield control, covering your retreat, or any other situation where you might want to create difficult terrain or slow people down. While the DC 10 Dexterity check is fairly easy to pass, all it takes is one or two people getting tripped up to clog an entire hallway.
But ball bearings have other uses beyond this. You can use a handful of them to detect sloping passageways, drop into an unknown liquid to determine if its acid or agitate any beings who might be waiting for a surface disturbance to strike, cause a distraction, or (my personal favorite) add them to explosives to create a makeshift shotgun or claymore mine in conjunction with spells like Shatter, Catapult, and Explosive Runes.
You don't want to lug around barrels unless you absolutely have to. With a cost of 2 gold, and a weight of 70 pounds, these are heavy and unwieldy items. That said, there's no better way to secure the mass-transport of large quantities of liquid, and by the time you hit mid-level, you're likely to have a wagon or other means of moving a lot of gear. For quests which take you across long distances or through deserts, there's nothing like having a few barrels to ensure a full supply of drinking water along the way. Your Cleric or Druid might be able to Create Water out of thin air, but they need a target for that spell, and nothing works like a barrel.
But barrels aren't just for transporting liquids. Made out of wood and banded with metal, you can use them to store sharp things that aren't suitable for stuffing into other types of containers. Confiscate a load of enemy gear that doesn't need to be sorted right away? Dump it all in a barrel. Need to move a supply of weaponry from one place to another easily? Stick them in a barrel, blade pointed down, and you won't need to worry about getting jabbed while moving them. Nails, caltrops, ball bearings--anything small, sharp, or annoying can be stored in a barrel for ease of access.
Barrels can also be used for offensive purposes: weigh them down with rocks and roll them down hills at oncoming enemies, or take a page from The Hobbit and use empty ones to transport yourselves down a river with a strong enough current. Knock a hole in one, fit it with a spigot, and you've got an easy way to lay down a trail of oil or gunpowder. Pitch, a thick, sticky substance which catches fire easily and is often used to coat the ends of torches to help them burn better, is commonly stored in barrels. You could use an empty barrel as a way of transporting one or more Tiny or Small creatures that might not otherwise fit into manacles or could slip free from ropes. And, of course, you can hide in one if you fancy Solid Snake is one of your descendants.
Barrels hold 40 gallons of liquid, or 4 cubic feet of solid material.
Think of a basket as a way to transport smaller items that you don't necessarily want to lump into a backpack or sack, but still want easy access to. Use baskets for holding foliage, spell components, alchemical reagents, or other lightweight objects like produce. With some string, a stick, and a bit of bait, you can rig up a trap for capturing small game or you can string it across a stream to capture fish or other sea life. Baskets, being naturally breathable, aren't suitable for transporting liquids, but can be used to store critters like insects, worms, and the like. You could also coat them with wax or dip them in pitch to create emergency liquid storage or set them on fire (though at 4 silver per basket, this isn't the most efficient use of your budget when it comes to light sources).
A basket holds up to 40 pounds or 2 cubic feet worth of stuff.
Obviously used for sleeping, you can combine a bedroll with some rope for a handy way to immobilize a prisoner by rolling it around them and tying it closed with some sturdy rope. Used the same way, it can pad one or more fragile items you want to make sure reach their destination in one piece, or hide items you'd prefer the cityguard not discover with a cursory inspection. After all, how many times during a campaign have your PCs been asked to unroll their bedrolls by the town guard?
A one gold expenditure all but the most rugged survivalists should have on hand.
Affixed to some twine or string, a bell provides a nice, low-level and low-cost alarm system which any Rogue should be able to set up and disassemble quickly. Apart from this, bells can be attached to prisoners' feet or hands to warn of impending funny business, used for non-verbal signaling over short distances (especially in conjunction with whistles or other noisemakers, where each one can have their own specific meaning: "If you hear the bell, sound retreat; if you hear the whistle, press the attack!"), or in the performance of various ceremonies.
Aesthetically, you could hang them from tree limbs or in windows for a chime-like effect if you so pleased.
For five silver pieces, a blanket provides some of the most robust usages of any mundane item in the PHB. Beyond the obvious usage of keeping an adventurer warm on a cold night (or cool in warm weather if enhanced by Prestidigitation), there are a million and one things you can do with a blanket.
Immobilize or temporarily blind a foe by throwing it over their head in combat (it only weighs 3 pounds, making this ideal to combo with a Mage Hand); wrap it around a fragile item you want to transport; use it with some wood to create a quick splint for a broken limb; roll it out on the ground to create a clean surface for dining or as a makeshift altar; use it in conjunction with another person to create a stretcher for transporting someone injured; wad it up and use it as a pillow; wet it down to help extinguish a fire; cut it into strips for bandages or as kindling to help start a fire; soak it in oil and set a burning candle on it to create a fire hazard; shelter under it from the burning sun or as a lean-to to keep most of the rain off; use it with a campfire to send smoke signals; roll up sharp things inside it to keep them from cutting you while you move them; roll it up and wet a corner--if you've ever snapped anyone (or just the air) with a wet towel, you know just how loud/annoying this can be; use it as a surface for writing a message meant to be seen from far away; fold it and throw it over barbed wire, brown mold, or other dangerous surfaces/terrain to pass without damaging yourself; pad metal items prone to clanking to keep them quiet while sneaking around; a source of multiple blindfolds/gags for any hostages/prisoners you have taken; wet it down and wrap yourself in it to provide protection against falling sparks or embers; pair it with spells like Prestidigitation and Thaumateurgy to scare gullible viewers; get enough people holding it and you have a makeshift landing pad for someone jumping out a window, or a way to get enough leverage to chuck a small creature like a gnome or halfling into the air to reach a window or ledge which is otherwise out of reach; hang it up like a curtain for some privacy while you seduce an NPC; wet it down and wrap it across your mouth and nose as a makeshift gas mask, or use it dry as facial cover during a sandstorm; black blankets thrown over you create great hiding places in shadowy forests or other areas of murky darkness...you get the idea.
For five silver, you should always bring along a spare blanket or two.
Block and Tackle
This device, when properly rigged, allows somebody to lift four times their normal carrying capacity. While not strictly necessary during most ordinary adventures, I guarantee at some point in your career, you're going to wonder just how the hell you're supposed to get some heavy piece of furniture or statue out of a dungeon or across some hazard (or pull some dumbass out of a deep well), and that's when you're going to wish you had that block and tackle.
Even if the DM ignores encumbrance rules in most situations, there will come a time when knowing exactly how much a given character can lift or push around. Unless they're exceptionally large, or exceptionally small, a PC can carry 15 pounds of gear per point of Strength they have, and they can lift/shove around double that (or 30 pounds per point). This means an average character with 10 Strength can comfortably carry 150 pounds of stuff, and lift 300 pounds. With access to a block and tackle, however, that 300 pound limit is quadrupled to 1,200 pounds...and we're talking about an average character here--imagine what happens with a 20 Strength Fighter or Barbarian yanking on the rope (no, I won't make you get out your abacus, it's 2,400 pounds).
A book, in this case, can be anything except a spellbook. Personally, I like my characters to keep some kind of journal once they have the funds necessary to invest the 25 gold, but that's just me. You could have a book for any number of role-playing reasons: a Bard might keep one of songs, poetry, or folklore; a Fighter might have a treatise on strategy and tactics (think Sun Tzu's The Art of War); a Monk or Cleric might have a copy of the tenets of their order or faith, or a book of philosophical sayings attributed to a famous leader; a Warlock might have a small work of eldritch symbols or invocations to their patron; a Rogue could keep one with a 'hollowed out' section for carrying contraband; the Paladin might keep a 'Book of Deeds' or other sort of record noting all the things their friends should atone fore after the current adventure has concluded. And, of course, in an emergency you can tear out the pages and use them as kindling (though there are far cheaper and better ways of acquiring flammable materials).
Books are more stylistic choices than anything else. Use them to customize the RP aspects of your character, or keep them to present as impromptu gifts to nobles or other sorts who might be amused or delighted with such an unexpected present.
And what do we carry in a bottle, class? That's right--any of those weird, unidentified liquids we come across on our travels that we want to experiment with, identify, or drink later. At 2 gold apiece, they're expensive but they're also the safest way to transport liquids you need to keep separate from one another.
A glass bottle can also make an impromptu weapon, be shattered on the floor to create dangerous walking surfaces for shoeless individuals, or hurled against some hard surface to create a noise or distraction. A bottle holds a pint and a half of liquid, and that could be anything from obvious stuff like water or booze to truly repugnant substances like blood, poison, even green slime or grey ooze.
Nothing lets you weaponize a Dungeon Master's own bullshit like a bottle.
Buckets are one of the most important items in the game, especially when it comes to siege defense, but somebody in your party should always have one at the ready in case of a sudden need to dump three gallons of liquid on something or someone.
The obvious use for a bucket is in conjunction with water to extinguish a fire, but nothing says you can't use one to splash a bunch of oil or slop some pitch down all over a wall or floor to create some kind of extra-flammable surface. You can also upend a bucket to capture a tiny creature like a rodent or large insect, cover a lantern or other light source, without extinguishing it or drop it over somebody's head to temporarily blind them. In fact, a bucket combined with Mage Hand can be a terror on the battlefield if used to dump oil on foes or extinguish their light sources (assuming you can see in the dark).
Buckets can even be weighted with stones or bricks and used to hold down pressure plates or as doorstops to keep something open or closed as needed. And who can forget the classic 'bucket of water on top of the slightly open door' prank? You need a bucket to do that, so all you would-be tricksters, make sure you've got one of these 5 copper piece wonders on you at all times.
I'm going to end it there, but come back next time as I root through the Player's Handbook equipment list starting with 'C' and continuing the chaos. This one's for you, @methus. Happy reading!