As patsu mentioned, Lumines Time Trial has been horribly addictive to me - I think I sunk 30 hours into that on the PSP alone. There are few simple games like this in which you can improve for such a long time. Make sure that you get Lumines 2, not 1, as the second game is much more responsive and nice to work with.
I also liked Daxter a lot, and it lasts you a good while and has pretty varied gameplay. And looks pretty!
Burnout on PSP is also very good, great in single player, and if you meet someone else with a PSP even more fun (gamesharing).
Final Fantasy: Crisis Core should last you a long while
There are a few more good RPGs, that I'm sure others will have mentioned or mention, but FF is actually the only one I have played.
God of War and MGS (both the proper and the Acid games) are also good of course. God of War just came out on budget, too. Prince of Persia also recently released a dual-pack. I played the first PSP one a fair bit and enjoyed it quite a lot actually. This is particularly good if you haven't played these games on the consoles yet.
Love LocoRoco also, obviously, though I'm not sure if I prefer LocoRoco 1 over 2.
Final Fantasy Tactics should be good, though I haven't played it. There are also PSone games on PSN such as command and conquer, though I don't know how good those are on PSP.
I still like Tekken on PSP a lot too.
There's a really lot out there now, but most of these are games that I have played myself for at least 8 hours
.