The hugely popular Djay app now has a video-specific brother, Vjay. This looks like a really well designed Video Remixer, with a clean interface and some nice transitions and effects. It comes with a handful of videos, but it also supports your own video library as well as anything you've bought on iTunes.
There is an introductory offer, bringing the price down 50% to $10.
It is unfortunately limited to iPad 2 or later, but this is hardly surprising considering how much processing must be going on to be tweaking video in real-time. The hardware support for Numark's goofy iDJ Live is a nice touch.
You should seriously check out this short intro video to see it in action.
All in all a very cool app, I look forward to seeing all of the YouTube videos this will spawn!