My most prized DVD is probably the special edition of The Royal Tenenbaums. I also have the special editions of Labyrinth, Big Fish and The Last Unicorn, and I'd be sad if they were gone.
I don't think I have any VHS tapes anymore. The one I always liked the best out of my family's collection was our super old black and white version of King Kong, where you could press on his chest and he'd let out this crazy awesome gorilla call. I'm pretty sure it's been torn to shreds over the years or lost in moving, though
Also, after I moved out, I used to carry a VHS copy of Alice in Wonderland with me everywhere I moved, but I got rid of it when I realized I'd probably never go back to VHS.