When you say you want others to make changes, do you mean clients or the general public? Most, if not all, CMSes have login areas where people can log in and make changes, but generally, you wouldn't want this to be open to the public. Sites like YouTube—which let people set up accounts and upload their own material—are pretty big operations, so it's a lot to take on if you are giving public access.
OK, cool. Any of the big CMSes would be fine. I personally use ExpressionEngine, which is great (and I find very easy to work with) but is has a price tag on it, so you may prefer something free, like MODx, Drupal, Textpattern, Silverstripe, CMS Made Simple, Concrete5 ... any of these would be fine.
I can only really speak for the one I use (EE). It would be very easy once the system to adding/switching videos were set up.
Another thing you could do—completely different, really—is to use a separate add-on for your site, such as Slideshow Pro Director. I've just been using it recently, and it's pretty good. You can set up slideshows, upload videos, etc. and manage them in many ways. The people uploading/managing the videos wouldn't have to touch the actual site at all. You would just set that up beforehand to display the videos in any way you choose.
Slideshow Pro has the advantage that it includes code that makes the videos viewable cross platform, which is really handy. Using SSP would also mean you won't have to rebuild your site with a CMS.