The very popular World of Goo has finally been updated with support for the iPhone 5's 16:9 screen (via Macgasm).
The $2.99 puzzler, which our sister site TouchArcade named as iPad Game of the Year in 2010, has players manufacturing bridges and towers out of balls of goo to help other balls of goo reach a particular end point.
At first, World of Goo is about manufacturing bridges and towers with the stretched tissue of little balls of goo. The point is to provide a path that other goo balls can follow into a metal pipe, the end point. Physics play a key role in this process: you'll need to build sound structures, which sounds easier than it is. Goo isn't concrete.
Each level requires a set number of goo balls to reach the pipe, and each goo ball you use for a structure counts against the total provided. This constant negotiation of goo resources is pleasing because it forces you to think around the obvious solution, which is often one of brute building.