Sort:  

Most cryptogames require at least a small investment. Eth.Town is a game that revolves around investing in virtual real estate assets and selling them. However, I believe you can achieve a lot already starting with just a couple dollars worth of ETH.

It's not as horrible as Cryptokitties, which is just a pure moneypot. You can also try participating in contests to win some free heroes, do things with them in-game and progress in-game without investment. This is a pretty large contest going on now and you don't have to invest anything to join it: https://steemit.com/gaming/@siddartha/ethtown-the-crazy-new-dapp-10-hero-giveaway

I wish you a lot of luck ;)