On the surface it looks like a simple Tetris / Lumines clone, but it's got depth. You need a bit of maths smarts to start clocking up high scores, because you're strategically placing numbered discs to eliminate grey ones, but it all starts to 'click' soon after you start. Even better, the game saves your progress whenever you minimise the app, so you don't need to restart your levels.
The king of side-scrolling shooters - on mobile at least - and it's free. The touch controls really work for both shooting and movement, and the coin-collecting brings an extra dimension to the action. It's available on iOS and Android, and if you want to pay money for it (because you're a 21 century Croesus), you can grab it on PSN too. #23Simpsons Tapped Out
When it works, Tapped Out is one of the best games on iPad. It's a little like Sim City, except your city is Springfield - which you rebuild after Homer triggers a nuclear meltdown. The beauty is in the details, and here there are stacks of authentic Simpsons stuff to play with. It's free for a few hours, but you'll need to invest cash to really get involved. On the plus side, you can also visit your friends' Springfields and either help out or - more fun - wreck up the place.
It's a little like Age of Empires Online, but for your phone or tablet. There are plenty of strategy games on the App Store and Marketplace, but this one gets things just right because it creates a great mix between building, grinding and multiplayer combat. You can do well for free, or boost your resources with gems.
Simple idea. You draw something suggested to you by the game, then someone else (friend / total stranger / enemy) guesses what it is by unscrambling a simple anagram. Amazingly, you don't see many comedy penises here, which speaks volumes for the sensible community you get matched up with. One caveat - it's easier to 'win' on iPad than iPhone because you're given more room to draw using your massive sausage-fingers, obviously.