Media Centre PC and Retro Console Emulator
The main purpose I have for the Ouya is to stream media to my TV. Recently, the PS3 has been OK, but with Cinavia watermarks being added to many new movies (and I imagine TV shows soon), the PS3 is not a good streamer for me. The Ouya will have more than enough processing power to playback 720p/1080p video in nearly any format.
I also plan to use Ouya as a retro emulator. Android emulators already exist for nearly every previous gen console, so it's not going to be difficult to get those operational on the Ouya.
For $100, it's going to make a great, flexible device for my TV. And if there are any great Android apps it can run, then I've got even more reasons to use these puppy. I hope YouTube is better on the Ouya than the PS3 as well.