Yes you can. It's a tethered JB (you have to plug in the cable to perform the JB and you'll have to rejailbreak anytime you reboot your phone) but it's better than nothing. It uses redsn0w 1.7
If you are on a iPod touch second-generation, you'll be able to jailbreak fine. If you are on a iPod touch third-generation, there is a tethered jailbreak available.
Games - yes.
Use redsn0w for iPod touch 2G or sn0wbreeze for iPod touch 3G.