The term ICO means "Initial coin offering". It basically means that you can buy into a new cryptocurrency / asset / token before it is created, usually with a very low price. For example if you bought ethereum at its ICO (I think in 2014), one ethereum would have cost you approximately 50 cent. Now the value of ethereum is more than $200.

So what types of new ICOs do I think you should look out for?

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#1. Decentralized systems that manage computations

You can offer computing power for others to use and get payed in tokens, or you can spend tokens to utilize others computation power. There will always be a need for computations, and with the decentralized model it will be possible for organizations such as universities to do heavy computations without buying expansive supercomputers that will be unmodern after some years. Instead it is the individual computers in the network (maybe called farmers in this case) that is responsible for upgrading themselves.
Examples of such ICO's so far has been: Golem, IEX.EC and SONM. In fact I think the price of IEX.EC is lower now than at the ICO.

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#2. New anonymous/untraceable cryptocurrencies.

There will always be a need for anonymity, and the investment opportunity for new anonymous coins should not be underestimated. I usually divide the types of anonymization methods so far into three generations:

Coinjoin (example: DASH)
Cryptonote (examples: Monero, Bytecoin)
Zerocoin (examples: Zcash, Zcoin)

Zerocoin is by far the most sophisticated way to create untraceability so far, using zero-knowledge proofs. These proofs basically prove that all inputs = all outputs, i.e. no double spending, but without revealing anything else then that, including who sent what to who. In Zcash even the amount sent is invisible.

Basically, whenever a fourth generation in the above list pops up or better implementations in the third, it might be a good investment opportunity.

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#3. Decentralized cloud-storage.

There will always be a need for storage space of information, and the decentralized version of it offers an encrypted, unstoppable, censorship-free and private way of storing information on other random nodes for a fee in tokens. Also you can get paid in tokens if allowing others to store stuff on your harddrive. Examples of such systems would be: Storj and Maidsafe, however Maidsafe seems somewhat directed towards not just storage space, but "decentralize everything", i.e. websites etc. You should also look into filecoin, however I'm not sure how it works and if it is in this category.

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#4. Decentralized exchanges

There will always be a need for exchanging between different cryptoassets, and the problem is that the exchanges themselves cannot be trusted due to their centralized nature. Decentralized exchanges offers a theoretical solution to this, but I'm not sure exactly how it would work or if it is even possible. But it is a cornerstone in creating a functional future space for cryptos, so be sure to look into this. Example: NVO.

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#5. Ethereum-like systems that offer alternative properties of the machine-language.

Ethereum is basically a "decentralized world computer". It has the property of being turing-complete, i.e. anything that can be calculated can basically be programmed into ethereum. There are however languages that offer properties that allow for general rules of knowing in advance that a program will behave within certain parameters. Those languages cannot be turing complete.
In turing complete languages there is for example no general rule for knowing which programs will eventually halt (as proved by Alan Turing). I think these are very foundational types of systems that will be necessary in the future. Examples: Boscoin, Tezos.

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ICOs that I'm not interested in

#1. ICOs of the type "yet another system for managing crowdfunding in a decentralized manner". Basically ICO's that want to create a new platform for ICO's (!)
#2. ICOs that claim to bridge the gap between the cryptospace and banking in some sort of all-encompassing solution, including "yet another bitcoin-plastic card".
#3. Gambling ICOs.
#4. ICOs that simply dont't make any sense.

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Sites that compile new upcoming ICO's

https://www.icocountdown.com/
https://icotracker.net/
https://www.ico-list.com/
https://tokenmarket.net/ico-calendar

What to do if you miss a crowdsale?

Sometime, after the crowdsale is over some exchanges start selling these tokens or IOUs, sometime at a lower price than at the crowdsale. However, keep in mind that as long as you are required to keep them at an exchange, they are not safe, so don't buy too much until you can transfer them to a wallet, for example an ethereum wallet if it's an ethereum-based token.