These were the responds I received from my original posting:

I was wondering how people handle posting students' video. We have a teacher who is working with students on a Capstone Project.  She videotaped the students' mid-year presentations.  It would be great to be able to post the videos, so these students can view them with their faculty advisers or be viewed by the members of the Capstone committee.  The students have been using a digital portfolio, but the portfolio can't handle the size of the video.  One option is to post them on YouTube, but keep them as private. What are you using to post student videos?

Teachertube

I created an account with TeacherTube and post videos there.  It is accessible from school and works much like YouTube.

We use schooltube.com - I've tried to interest admin into purchasing a channel ($500) but in the meantime it's easy to post. It's possible to keep it closed (unless that's changed). I also asked the students who videos they were if it was ok to post. It's a monitored site - you can be the monitor & other teachers could too. 

I use school tube, and choose the option that "just my school" can see it. 

Then I post it to my website on a password protected page.

I like the YouTube option

I have posted some on facebook. You can do this on a closed group.

We use Vimeo and password protect it.

We have students save them to their google docs and then share them as a link on their google site.