I am a big fan of The Room, an iOS app which has gained plenty of accolades here and elsewhere already. One of the most charming things about The Room, I think, is how well it replicates real-world objects on a touchscreen platform. The Room expertly turns the touchscreen interface into a series of mysterious puzzle-boxes, all very fascinating and ingenious to play with.
Interlocked is another app that does that, although without a lot of the extra mystery and setting that The Room adds to things. The app is published by Armor Games, the same company that published the great Kingdom Rush, and like Kingdom Rush, it's based on a popular Flash game you can play for free online. Also like Kingdom Rush, the iOS version has been polished and cleaned up a bit.
The game is simple: You're given a puzzle with a set of interlocking pieces, and then you can drag or swipe around the screen to try and pull all of the pieces apart. The game starts off easy, and quickly gets difficult -- just a few levels in, I had some frustration trying to figure out just how these pieces on screen fit together. If you're a fan of these kinds of manipulation puzzles, you'll love this setup for sure.
As I said, Interlocked is a pure puzzle game, so it doesn't have any of the mysteriousness that made The Room so popular (and if you haven't played that one, you should). Still, if you like these very physical puzzles, Interlocked, with plenty of content and a nice clean interface, should offer up lots of fun. It's available right now as a universal app for US$0.99.