The Shawshank Redemption was the first title I thought of when I read the thread title.
Another one that I find myself watching even though I own the DVD is Million Dollar Baby. Whenever it's on HBO and I'm checking the listings, I always put it on and watch for at least 5 minutes.
Other than that, if it's a movie that I own on DVD and want to watch it right away, I'l get up and pop in the DVD.
I have hundreds of them on DVD, yet if I'm just flipping channels, eating breakfast, reading the paper, etc. I'll stop on something I enjoy.
What's really amazing is that even owning the DVD, widescreen, great sound, etc. I'll sit and watch a horrible full screen, pan & scan version, edited, time compressed, and with commercials.
TCM and FMC being the exception, and HBO is not edited, but still P&S.
I rarely watch the entire movie, but just seeing my favorite portions is enjoyable, no matter how bad the presentation.
Back to the Future(s) Ferris Bueller's Day Off Down Periscope National Treasure So I Married an Axe Murderer Empire Records The Sandlot ...probably more I can't think of right now.
Legally Blonde...sort of. I swear TBS shows this every week but I don't usually watch it completely every time. I'll come back and check in to see my favorite scenes.
Ones I will sit and watch them through again and again, though...
Rio Bravo The Quiet Man The Silence of the Lambs Back To The Future Part III (I've tired of the first 2 chapters, but as a westerns fan I still get a kick out of part 3) El Dorado
Judgment Night. I've been watching that every time I see it on since it debuted on cable. The Principal, though I rarely see it on any more. The Breakfast Club.