Certain phone types have their own game hubs, but there isnt a dedicated one for android itself.
Below is a list of the stuff i mainly play. I have WAAAAAAAAAAAAAAAAAAAAAAY more games for android but these are what i have on my note at the moment. Another tip though, is watch the Humble Bundles. Occasionally they do android bundles and you get some pretty sweet games from there for cheaper than what youd pay on the store for one of them.
I mainly play Plague Inc on my note 2. Its kind of like Risk, only with different types of plagues that you unlock as soon as you win with the previous plague. Simple and fun but can be quite hard if you dont plan your moves and timing right. Free, but you can unlock a few bonus features and stuff through microtransactions.
store link
Another cool game i play is a gears of war style online shooter called ShadowGun

eadZone. Online deathmatch style game, needs net to play though, so wifi is recommended. A few lag spikes here and there but an awesome game all around. Free
Link
If you like online card games you can play either Cabals or ShadowEra. Both are SP or MP based collectible card games. Kind of like a mix between Yu Gi Oh, magic the gathering and Duelmasters. Both are fun and both are free.
cabals
ShadowEra
If you like zombie shooter games and dont want to buy CoD: Zombies, you can get Dead Trigger. a fast paced zombie survival shooter. Great fun, though weapon progression is based heavily on micro transactions. Still great fun though and it has co op.
link
If you are a fan of minecraft, you can get the pocket edition for R50 odd off the store. I never played minecraft cause i thought it was stupid. My mate sat me down and made me play it on his note and i went the same day and bought it for my note, then got it on PC... then got it on Xbox... I LOVE it and its a cool time sink if you get your creativity on.
demo link
If you are looking for an online, WoW type game, Arcane legends is freakin awesome at the moment. It a free MMO, also with micro transactions, but they arent really needed. A bit difficult to get together with mates and play, but once you do it great fun
link
If you like Dota style games, granted its a MASSIVE download, Heroes of Order and Chaos is BRILLIANT
link
AND FINALLY!!! My absolute most favorite game of all time... Beat Hazard. If you get seizures from bright flashing lights you shouldnt play this, if you dont, PLAY TEH SH!T OUT OF IT>! Its a space invaders/rtype rhythm game that uses your own music to play. The faster the beat and tempo, the faster the gameplay becomes. amazing fun and listening to music at the same time is a win.
I recommend the paid version for this.
link