Bloodrage increases all damage dealt to/from a hero. This means that spells and items will also deal increased damage if a hero is Bloodraged.
Bloodrage bonuses are halved if a target is more than 2200 range away from the dealer.
You can Bloodrage allied or enemy creeps right before they die and lifesteal off the last hit if you don't want to risk casting it on yourself.
After level 3 Bloodrage, you can cast the spell on yourself and a target to double-heal when you kill it.
Bloodrage can be used to pop Linken's if enemies are trying to block your Rupture.
Bloodrage works on Roshan. Please warn the person who's tanking Rosh before you use it, though.
Enemies can't easily use Blink Dagger if they're Ruptured. It has a pretty long cast range and the debuff lasts a ridiculously long time, so it can be useful to perma-cancel a Blink from an initiator like Tidehunter or Magnus before a team fight begins.
Blade Mail can be a worthwhile pickup against Lotus Orbs to force a target to take Rupture damage if you have HP to burn.
Counters
Consider getting a Magic Stick against Bloodseeker. Chances are he's going to be spamming Bloodrage like crazy in lane and each cast will give you a charge.
Get a Mek or Urn on your team and carry around lots of regen. If BS isn't getting Thirsty in team fights, he can't deal much damage.
Blade Mail can be good if you're tanky, especially if he Ruptures you.
Lotus Orb can provide a lot of value when placed on your carry since BS will feel uneasy about initiating a team fight with Rupture.
Rupture won't damage you if you travel >1300 units in one tick. This means that talents that increase your cast range or Blink distance can counter Rupture.
Remember that he's taking a ton of extra damage if he has Bloodrage on, so don't be afraid to fight back.
Kiss juking goodbye if there's a Bloodseeker on the enemy team. Once a match you'll find yourself wondering, "HOW DID THEY KNOW I WAS THERE???" Then you'll look up and realize that Bloodseeker was giving his team global vision of your ass when you're under 25% HP.
In the same vein, be extremely careful when jungling against an enemy Bloodseeker. If he detects you at a dangerous HP, you can be sure that his whole team will be trying to score a kill on you.