Download Mahjong, by Clockwatchers Inc, from the Google Play store. The game is free, and runs on Android 2.3 and up.
In Mahjong the rules are simple: someone has intricately arranged a collection of tiles. You need to match pairs which are not trapped by other tiles, progressively erasing tiles from the board. Clear the whole board and you win. Can you do it?
Ultimately, Mahjong games come down to several factors: the variety of layouts, the aesthetics of the tiles and how well they replicate authentic Chinese mahjong tiles, and how solveable the puzzles are.
Mahjong can be tricky, but like all good games there are strategies you can employ. For one, look over the board and if you can see four matching tiles that are available to be removed then get rid of them all at once. There are only four copies of each tile, representing two pairs. A second tip is to generally favour freeing up tiles. If you have the choice between matching tiles on the top of a stack or loose-standing tiles, go for the ones on the stack as this exposes more tiles.
If you haven't played Mahjong, or you have been looking for a good one for Android, then this game is for you.