Stabilizing GoPro videos
Software that I know of:


Virtualdub with Deshaker plugin:
http://www.guthspot.se/video/deshaker.htm
Sony Vegas Pro since version 10 has a built-in stabilization plugin
Depan for Avisynth - http://avisynth.org.ru/depan/depan.html - it can get quite complicated but there are sample scripts to help getting started.


Youtube can detect if the footage is shaky, though it's not always working so well and it applies to the whole video.
My personal favorite is the Virtualdub route. Just remember to save it to a lossless format if you plan on editing it further.