"Last Friday YouTube rolled out its new on-site editing service, YouTube Remixer, powered by Adobe Premiere Express. ...YouTube Remixer is exactly the same as Photobucket’s Remixer (previous coverage here), except that Photobucket launched theirs back in February and it has far more features."
It's not nearly as good as Windows Movie Maker or iMovie, and you have upload to an error prone server, but it would allow someone to make a mashup from stuff they got from the net. I remember liking Jumpcut better, but it's been awhile.
Mashable says they've covered other web-based video mixers including Gotoit’s PowerSuite, Mojiti and Eyespot.