Short and sweet:
Whenever you only have about 20-30 minutes to piss away, what game do you typically play to pass the time?
Lately it's been HarmoKnight on my 3DS but usually if I just have a few minutes I whip out my phone. That list of games changes a lot but a few I come back to frequently are Super Hexagon, Infinitey Blade, and Knights of Pen and Paper.
Rayman Legends on the Vita and Half Minute Hero for the PSP.
It actually tends to be whatever I currently have in the disc tray. Right now that is Crysis 2.
Usually Contra or Double Dragon. Big surprise right?
Super Meatboy.
Short yet tough levels make it easy to find a stopping point by either beating a level or rage-quitting.
with just a little bit of time and programming every waking moment, I've mostly been playing Anno Online, which is a browser based game you can leave alone for hours. I click on it, sort out some commands, then go back to what I'm doing. It's really relaxing though to take a break and work on my town.
SNK classics: metal slug, samurai showdown, fatal fury, shock trooper etc (if I'm on the PSP) or any beat em up that takes my fancy (at the moment Naruto: Ultimate Ninja storm 3 or MVC3. Good times.
Borderlands 2 is one of them. But if time is limited I often do a little multiplayer on COD:Black Ops 2. Most matches last less than 10 minutes,so it works out well. Gives me a quick game fix!
Pokemon Pinball. Easy to pick up and put down.
Borderlands 2, FIFA those are usually my go to's for a quick game.
Pokemon because I can save anywhere when you're not battling, or Mario.
At the moment, I play Fairytale Fights. It helps me relax especially if I have had a tough day at work.
Minecraft. Also, any tower defense game.
Lately that would be Borderlands 2. Its just enough time to raid the gold key chest a couple times. Or putting in some pratice on Blazblue Continuim Shift, my new favorite fighter.
Only 20 - 30 min? Why bother? I guess I could take out a handheld game. 
Mario sports games are fun to play for a short session. Or Mario Kart. Honestly, though, I just play whatever I feel like playing.
20-30 minutes I'll probably look up gaming news on the internet or something. I would normally load up Halo Reach if I got an hour or so to pass, but with only half an hour I might not even finish a match!
Angry Birds. What! Stop looking at me like that!