The platforming is awesome for one, but the basic idea of entering people's minds is just genius. I love it because the the characters are all memorable in their own sort of way, like Dogen, who is the coolest character in the game. It's the little touches too, like getting the ability of clairvoyance and seeing what people really think you look like to all the safes that are locked up in people's minds that you open up and learn about their pasts. Mila's suppressed emotions are one of the scariest things I've ever seen in a video game.
I won't argue that Psychonauts is perfect, because I think that last level is horrible. But once I was thrown into the Lungfish City, the Milkman stage and when you enter the Bull-fighting stage, it was hard for me not to get hooked. It's one of my favorites, no doubt.