There was a time once when you couldn't get on any public transport without seeing at least one person playing Angry Birds.
For me, the absolute pinnacle of Android Gaming is the Walking Dead game but I love a lot of the part puzzle-part adventure games too. G5 seems to have the best of these. If you follow G5 games on facebook, they often have free versions of their full games for a limited time. They also have a lot of "specials" and of course if you just want to try their games, there's always the free to play trial versions.
Some of the standard puzzle games on Android are pretty good too.