If you want the vids hosted by others, then there are lots of options again, YouTube being the most obvious, but also Viddler, Vimeo, Blip TV and so on.
Yes, but that’s not what I was referring to. I mean that once the video is created, you have two basic options: either upload it to a video hosting service like YouTube or Vimeo and then link to the video from your website (it will still be able to play on your website, but will also be viewable from the hosting service itself if you so choose), or you can upload the video to your own web server (wherever your website is hosted) and use one of those video players I linked to (such as Flowplayer) to enable people to click “play” to view the video.