Wild Blood, Shadowgun 2, N.O.V.A 3 freedom, MC4 and 5, Ravensword Shadowlands, Blitz Brigade, EA Real Racing (can i use the stick to shift?), and Snowboard Party. These apps have all had trouble on my mbox and are my justification for going ahead with the shield how's your experience with these apps on the shield tv?
I don't have the Shield TV, but I do have a Nexus Player and I can say that most of those games are not compatible. I can't say it will be the same for the Shield, but most apps just aren't compatible with Android TV.
Here is a list of games that are available on Android TV. It doesn't seem to be comprehensive as it does not list Modern Combat 5, even though it is compatible with my Nexus Player, but I wouldn't expect to find most games that are on Android.
If a game isn't listed as compatible you might still be able to sideload it, and as long as it has full controller support it will probably be fine.
http://shield.nvidia.com/games/android