This isn't an iOS port of the great Flash game You Have To Burn the Rope, though an upgraded version of that would be nice to have. Instead, this one is a pretty inventive puzzle title by a company called Big Blue Bubble. The idea is that you touch anywhere along a rope to start up a flame, and then you have to keep that flame burning by tilting your iPhone so that the fire always burns up.
It works really well as a physics puzzle game, and each level has certain percentage goals of the rope to burn (and later there are enemies to burn through as well), and whenever your flame splits off at different intersections, you need to watch each side of the flame and make sure it has vertical room to grow. Getting through the levels is not that hard, but burning everything on the screen is both challenging and fun (when you can actually do it). It's a really inventive game. Something only possible on the iPhone, it takes a nice different angle and just iterates on it, similar to popular games like Angry Birds and Cut the Rope.
That iteration lasts over 80 levels, and the developers promise even more to come. There's no Game Center integration, unfortunately, but there is a silly theme song, and all of those levels make for quite a bit of game. As of this writing, the game is on sale for a buck, but I think it's worth it even for a few bucks. It's too bad there's no lite version to try out, because the concept really is original. But if you like puzzlers like Cut the Rope and Zen Bound, this one will probably scratch that same itch.