Depends on my mood, and what hardware I have on hand.
Crypt of the Necrodancer is one of the best rogue-esques in my library, and for good reason. Music is good, so it scratches some rhythm itches, the rogue structure keeps is fairly repeatable without feelings painfully repetitive, and the dungeons are relatively short so it can be as short as 5-10 minutes if need be. Only flaw is public play almost necessitates headphones. Also good for netbooks, PSVita, and laptops.
Pocket Card Jockey has been on of my 3DS vices lately. It's unnecessarily complicated meta-horse racing built on top of a really simple Solitaire-style game. The better you do at solitaire, the better at running fast your horse is. There's more to it, but races take between 5-10 minutes and after the frustrating tutorial dialog, the narrative framework gets out of the way and play becomes readily accessible for easy pick-up-and-put-down play.
I won't dwell too long on the 3DS, but Animal Crossing: New Leaf, OlliOlli (also on PC), Mario Kart 7, Rhythm Thief & the Emperor's Treasure, Team Kirby Clash Deluxe, and WarioWare: Touched! are all good pick-up-and-put-down options.
Since the PSVita billed itself as a handheld console, a lot of its titles feel built to do longer-term sessions well at the expense of feeling as punchy. One of its ports fit handheld playing well, though. In particular, Zen Pinball 2, Need for Speed Most Wanted, CounterSpy, and Jet Set Radio.
So, in short, I play a lot of games that are easy to pick up for short sessions.