If it's a movie I really enjoy, I'll re-watch it once in a while, even if it's just a "one off" film like "Kingdom of Heaven" or "Scarface". I've watched a lot of Star Wars and Lord of the Ring over and over.
I'm yet to re watch any anime series as usually watching it once is enough for me. I usually watch it originally subbed in Japanese and I won't re watch the dubbed unless it's extremely good quality (very good voice acting,720p video quality.)
The only series I've watched which is technically a "remake" is Mobile Suit Gundam 00 season 1 and 2, but I never saw the original.