I like gaming but don't have the time or inclination to pad through a 30 hour in-depth game. I love the missions in GTA San Andreas but hate the repetitive nature of having to return to missions when I fail them, rather than just reply them. I'm sure many people love that immersive world but, for me... it's just repetitive. ERGO...I love my PSP, it's portable so I can play anywhere, including the potty which, I have to say, is a great place to sit and play a game...it's got a nice bright screen which the GB advance lacks and although it doesn't have as many 'different' games like the DS does, mine's hacked so I can play (ahem) 'homebrew' games and it's got quite a few mini games nowadays. By this I mean a game that contains several simple stupid games with very few keys to learn and which last maybe up to 5 minutes each. Do well on a game and you'll unlock a new minigame and so on.
Hot Pixel is one such game, it's made by Atari and has several (200ish) mini games. Some last as short a time as 10 seconds, others up to a couple of minutes. Some can be repetitive, i.e. same thing, different difficulty level but all are fun. :)
I think games like this are great as they begin to open up the gaming world to people who otherwise wouldn't play games.
If you've played Hot Pixel and enjoyed it, I recommend Kazook, Ape Academy/Ape Academy 2, Hot Brain and Work Time Fun.