OutRun 2006: Coast 2 Coast would indeed be an excellent choice for PSP gaming. Other good options for PSP racing would be Ridge Racer 2 and the two Wipeout games (Pulse and Pure). Maybe the Burnout titles as well, but I'm not personally familiar with those.
If you're into time attacking, then racing games are excellent for quick bursts. You can have a satisfying 10-minute session, or if you have the time, you can stretch it into an hour or more easily. I have to name-drop my favorite racing game Side By Side (PS1) once more, since it's exactly this feature that keeps me at it. A single run on a track lasts about three minutes, so even if I have to suddenly stop, I only lose that one run.
As for other genres that are good for a quick play...shmups can be good, though full runs of them can last anywhere from 20-60 minutes. But if the game has a stage select mode or a shorter gameplay mode (like Fire Arrow Plus
, it even advertises itself as a "coffee break shmup") then you can play those during shorter time periods. The PSP has a few good shmups to it, Star Soldier is pretty decent.
A single fight in a fighting game only lasts a few minutes usually, but those are usually better played against other people rather than AI, so your mileage may wary there.