This list simply wouldn't be complete without Clash Royale. From Supercell, the makers of Clash of Clans comes another hit game that's near the top of the charts month in and month out. It's extremely fun, addicting, casual, exciting, yet frustrating all at the same time.
Clash Royale is a real-time strategy and card collecting game. Using troops and characters from Clash of Clans (and then some) players will battle against others in real-time and try to outplay or outsmart their opponent. Take down a few towers and win the battle. Then earn chests to unlock more cards, collect them all, and upgrade troops.
While we wouldn't necessarily call this a "casual" game, as it's extremely competitive, I play it casually while sitting around the couch watching TV. If you have 3-4 minutes to spare fight a quick battle, unlock some chests, and wait a few hours to repeat. You can play as little or as much as you'd like, and it really doesn't matter. Making this one of the best casual games for Android in my opinion. Be careful though, you'll end up losing a lot and being tempted to spend real money on upgrades, so use caution and self-restraint.