Update 7/2/11: Big Blue Bubble released Burn The Rope+, which is an ad-free version of the game for those who don't like the extra permissions in the original game that are required for in-app purchases.
Burn the Rope has you, well, burning as much of a rope as you possibly can. However, the fire won't burn downward; it'll only go up. As a result, you'll be forced to tilt and turn the puzzle if you don't want the flame to die out (and trust me, you don't).
To add to the fun, some levels involve various critters that crawl along the rope. Depending on the type of bug, the effects on the flame could be as simple as a change in color or as complex as a web bridge, which will allow access to new parts of the level.
Best of all, the app costs precisely $0. If you want to grab it, simply scan or click the widget below - but be warned that it may take a while to download, as the file is 29MB.
Burn the Rope
Burn The Rope Plus