How is it random? Jut tell your friend you had a great tie on vacation and you would like to have the videos so you can relive it.
A friend of mine took videos and saved them, of me doing silly things while on vacation. I would like those videos, but I don't know how to ask for them without seeming weird or obsessive. Also, this was a few weeks ago so me asking is very random?
Really?
If they are your friend they shouldn't mind at all. Just tell them you want to see them. No harm in asking.