Some quality games discussion here!
On PC I mostly just play Dota2 and LFS. I play on android a lot when I'm not sitting on the computer though, and since it's hard to find good android software/games, here's some you'll want to consider. If you know of any gems that I didn't mention, please post.
I play on Samsung Galaxy S2. Out of these only Osmos makes my phone warm up a bit while playing these games. The others will likely perform well with a slower phone too. First the free ones:
Zookeeper Battle
Traffic Panic
Prepare to pay a pound or two if you get hooked up on explosions
Winter Walk
Sudoku 10'000 by 1gravity
Best sudoku app I've found so far. If you like Simple Sudoku on the PC, this is what you want.
Hexwalk
Netwalk with hex grid and nice looking graphics. Just try it.
Then there are some you might want to pay for.
EDGE
Demo linked for you, won't do a sales pitch
Osmos
Demo linked again. This one is not a game for those 2 minutes you have nothing to do waiting for the train. It's more for the 100 mile train ride when you want a nice little slow-action realtime puzzle game. Bring headphones for great soundtrack.
Flight Control
Demo. Do not accept cheap copies, NAMCO Bandai is the one.
Superbrothers Sword & Sworcery
This one's an art game tbh. It's like an interactive fairytale with great visuals and soundtrack. See trailer.
Another World
A game in great art style and atmosphere, but this one is actually hard in difficulty like the original in 1991. Some puzzle, some action. No language barrier at all.
Plants vs Zombies
PC casual classic on android.
Super Hexagon
This is the gem of all mobile games. Fantastic art style, awesome soundtrack that works perfect even on phone speaker, simple controls, addictive but not in the way that you would play it 30 minutes straight. In fact, your first game will probably last about 3-5 seconds. My best is still under 40 seconds in the easiest difficulty.