I suppose you could just call Psychonauts an action adventure platformer. It plays like a typical platformer but there are some "treasure chest" adventure elements where you can search for stuff and also the entire game takes place in a huge kids camp. The main action stages take place in the minds of characters and you gain neat psychic powers.
Its good fun, has a great sense of humor, funny characters, fun stages (except for the last which I didn't care for myself)..its all good really. Looks nice on the pc with all the fitering turn on at a nice high res.
I recommend it myself since I dig these type of games but if anything try out the demo.