I have a client which I've been working with on a site built on Asp.Net MVC 2 (although I don't think that plays too much into this question) that helps with their workflow from outside vendors. One of the features is adding a video tutorial for their users (who are not technical, and will likely use the site once).
Originally they wanted to embed a player (YouTube or another similar site) from which the video would play. One of their programmers though convienced them to host the video on their own servers.
I can only really think of bandwidth as a concern. The video in mp4 format is 400mb, and while the site is low volume now, they are adding more of their customers to use it which is why we're continuing to expand its functionality.
So, what other criteria would should be considered when making this decision and what would push a decision one way or the other?