Researchers at Microsoft have developed a method to make smooth timelapse video from head-mounted cameras. That sounds kind of boring until you see it in practice, and you get a taste of the technical problems involved. File this one under "Computers are Pretty Amazing."
In the first video, the researchers show the differences between the source video (super shaky head-mounted GoPro footage), a "naïve" timelapse (just pick every 10th frame and stitch it together), and their hyperlapse process. Be warned, you might get motion sickness if you watch too much of this (especially fullscreen—and it's not full HD quality anyway). Given that warning, behold the might of computation:
Want more technical detail? Oh, there's plenty in this extended version, explaining the lengths researchers had to go through to make this work. It involves deducing the path the camera traveled, choosing a new (stabilized) path, and combining multiple frames to make that path work.
There's more information on this method from Microsoft Research, including a technical paper (35MB PDF). If you just want to check out more cool hyperlapse videos, I recommend: Google Street View Hyperlapse; New York in Hyperlapse; and a collection of hyperlapse videos from around the world.