Both the PSP and the DS are great because you can flick them off at any moment in time, so even if the game itself doesn't lend itself to short bursts of play, the console still makes it possible. But for specific games... I'm surprised a lot of these haven't been mentioned yet, to be honest!
PSP:
Lumines (any version)--My favorite game on the PSP anyway, but for quick pickups, the 1 minute challenge is fantastic. I love to play a few of these during a commercial break in a show I'm watching. The game itself doesn't lend itself well to pick-up-and-play, but the 1 minute time trial is ideal.
Loco Roco--The game is extremely relaxed so in almost all cases, you can look away without any risk of dying, and unless you're doing a time trial, there's no pressure to finish on time either. Great relaxing game.
N+--go see
Infernal Monkey for further details!
DS/GBA:
Meteos--Like Lumines on the PSP, Meteos is probably my favorite game on the DS. There are several flavors of time trial in this game, I especially like the 1000 block launch (takes about 20 seconds a pop). But unlike Lumines, the whole game is exceedingly well-suited to quick games. If I'm bringing my DS somewhere, chances are this game is in it.
Rhythm Tengoku/Heaven GBA/DS--It's a super fun game and each song takes about 2 minutes at most to play, so it's very easy to pick up and play. Of course, you need to basically like music games and/or Wario Ware. Speaking of which...
Wario Ware--any and all, but especially Twisted, since it's so Goddamn fun it's almost illegal. As long as you don't mind looking like a ponce twisting your DS around in public (and, if you're anything like me, giggling like an idiot).
There's probably more games, but I can't think of 'em right now.
Jam it back in, in the dark.