I was thinking of something like: http://www.flickr.com
but I don't think you can upload videos (only photos?)
There must be others out there that know of a "remote media gallery".
I also looked at: http://www.picturetrail.com/
same thing ... photos, but not videos.
The other option would be to "tone-it-down" a bit ...
Come up with a simple upload script that puts images into
a directory and just displays them as a list of files. No MySQL,
no security (or not much). If you had some scripting skills,
like Perl or PHP and your webhost has "imagemagick", you
could do more ... but again, it involves some programming.
That's why it might be nice to just subscribe to a remote
gallery online service.