If so, what type? Do you save the final mix and a video file in a Pro Tools session?
Do you buy the DVD release or record it somehow?
Is it smart to keep a copy of everything you have ever worked on? Small and big?
I save everything (and I mean EVERYTHING) for at least a few years. Every once in a while someone turns around and says that something needs to be change. After 3 years or so, I'll go through old material and cull it down to a set of stems that will give a reasonable amount of flexibility on the off chance that I need to do something with them.
Afterall, storage is CHEAP nowadays.
I keep absolutely everything I work on. Older stuff is on DVD-Ram on the self, and lots of it is stored on a raw hard drive in a Hudzee box on my shelf. Products that have been completed and released I try to get a final copy of, but sometimes I don't. That's not as big of a deal to me as keeping my sessions and materials I used for the project.
At the day job, I pretty much have to keep everything because one never knows when a client is going to come back after 3 years and want to resurrect an old project. I think I have every session going back to when I switched from Sonic Solutions to ProTools in 2001. For my independent sound design work I also try to keep everything, though there are some projects where I ask the client to purchase a hard drive, and I let them be responsible for the assets. As far as released copies, I like to have at least one copy around. It's something I can show to my family so they have some context for what I do!