I found Final Fantasy VII: Crisis Core pretty amenable to short sessions. Many of the missions only take a couple minutes to complete, save points are frequent and of course you can suspend the PSP at any time.
Gunpey's also great for short bursts like Lumines, though I'll add Hot Shots Golf (either game works fine), Ridge Racer, WTF, Exit, and Crazy Taxi: Fare Wars if you're avoiding Lumines-like games. Puzzle Quest could be a good fit, too, but you'd likely not want to stop after 15 minutes.
[quote name='Ryuukishi']I found Final Fantasy VII: Crisis Core pretty amenable to short sessions. Many of the missions only take a couple minutes to complete, save points are frequent and of course you can suspend the PSP at any time.[/quote]
I was going to post that too. I leave Crisis Core in my PSP (still haven't finished it) and do a side mission from time to time. They are addictive, short and sweet. Plus the side missions really help you in the main storyline.