I don’t often play games on my iOS devices—they’re a bit too casual for my liking. The games that I do play are almost always puzzle-based: Letterpress and Words with Friends, among others, have stuck with me.
Lately, I’ve been having a lot of fun with “Threes!” I prefer to play it on the iPad, but it exists on all iOS devices for a mere $2. It’s not overly complicated, but at the same time, a bit tough to describe: you match up numbered tiles with other numbered tiles until you run out of room on your 4x4 tiled board. It’s incredibly simple and very addicting.
Also, for what it’s worth, the background music in this game is just phenomenal.