Yes, Games have been out on the zune since May. Microsoft released XNA Game studio 3.0 CTP for people to make games and deploy them on their zune. There are probably over 30 games for the zune and like 15 or more applications, like alarm clocks, book readers, ect.
Head over to
http://www.zuneboards.com/tip-of-the-week/how-to-install-games-on-your-zune.html to find out how to install games on your zune.
Here is where all the game for the zune are located:
Download Completed Games - Zune Boards
I made an installer for Xmonster so you don't need XNA Game Studio 3.0 and Visual Studios to instal it, but you have to alread have installed a game using XNA Game studio before you can use my installer... becasue the game studio puts the runetime files on your zune, so you zune can play games. After, that you can run Xmonster.exe and it will take care of installing it to your zune.
For other rig installer games go to
RIG: Games and applications for the Zune.