I checked out the LJ scrapbook, but it dosen't seem to offer what I'm looking for. I could certainly store the files there, but it dosen't seem to be able to embed the videos the way I could with either youtube or goggle video.
The last option seems to be photobucket but their main limitation is that they only allow videos of up to 5 minutes in length or 100 megs in size. Neither of those are going to work out in the end, even if it embeds it properly. Actually, I'm testing it right now. I took a quick and useless video a bit earlier and it just finished uploading. Lets see if it actually pops up from photobucket:
Hmmm. Well, it looks like it works. Another downside is that it took a hell of a long time for it to upload and that was a very short video. I might also run out of storage space rather quickly using it. I certainly wouldn't want to have to start paying for it.
Well, if anyone has any suggestions, drop a comment. I'm going to head over and see if Google Video is any better than YouTube.
Edited to add:
Google for the win!
It allows you to upload videos without having them included in search results, so you can basically only find a video if you're given a link or follow a person's id. That's what I basically wanted and it seems to be as good as youtube as far as the interface goes.