Here’s a lovely example of the kind of software people can produce when you expose the API for a nice system like QuickTime. iStabilize is an app which removes camera shake from video by analysing the motion and then moving the image around to counterbalance the vibrations. It does a very nice job, too – have a look at their demo movies.
You lose resolution, of course, because it has to trim the edges, but I tried it on some clips that we’d taken while running(!) and it did a very nice job. If you’ve got footage which is a bit bumpy, this may be the app for you… It’s $60, but it’s fun to play with in demo mode. And re-shooting your footage might be a lot more expensive…