YouTube does allow you to put a viewer to your videos anywhere on the Web, but otherwise, like most other video services, it's a closed system. Videos go in but they don't show up on other video destination sites. And videos from elsewhere don't show up on YouTube.
As far as I know, there's only one video system that both hosts video and searches video on the Web: Yahoo's relatively new Yahoo Video. Just like with YouTube, you can post your video to the Yahoo site and have it host it for you (although as I write this, the posting service appears to be broken). But Yahoo also searches other sites and displays video from them alongside its own. Even Google Video doesn't do this.
The one criticism I have of Yahoo Video is that it doesn't convert all video it finds into a streaming format. Some of the videos it indexes need to be downloaded to your PC before they'll play.
But overall, this is the way online media and search is supposed to work. It's maddening to have to scan multiple sites for a media file you know one of them has, and it's insane that video uploaders have to work around this problem by posting their video to multiple sites. Yahoo makes it possible to use just one site to find all content. That was the original idea behind Yahoo's Web search engine, and it still makes sense today.
There's still a lot to be said for hanging out on YouTube or any other site that features user-generated content (UGC), since how the community rates content and comments on videos is part of the experience. But Yahoo, because it allows users to both upload video to the site and to search all the Web for video, is much more than a YouTube competitor. It's online video the way it's supposed to be.