I once tried Tiger Woods golf on my friend's Xbox years ago, and I thought it was lame compared to Hot Shots 3 and 4. However, a quick google shows some older version for PSP, and I don't know how it fares. I can probably count the number of video games I've been addicted to on one hand, and Hot Shots is definitely one of them. I'm not a golfer, but this one taught me a lot about the basic strategy of the game, and the best part is that you get to talk crazy smack. When you beat new levels, you unlock better insults. A few somewhat-subtle-only-to-a-kid sexual remarks too. Ok, what I REALLY didn't like about the TG game years ago was that you could actually affect the flight of the ball after you already struck it. Where the hell is the realism in that . . .
I like "spatial" games like Tetris and chess, etc. The problem with Tetris is that you'll be seeing the blocks lining up in your sleep . . .