Oaky, so movies I will absolutely watch if I happen to tune in (no particular order):

The Hunt for Red October
The Thing (original)
Airport (original)
Forbidden Planet
The Day of the jackal (original)
The Bourne Identity (remake)

I'll definitely second as ones I will also absolutely watch:
Groundhog Day
Dr. Strangelove ("You don't think I'd go into combat with loose change in my pocket, do ya?"
Singin' in the Rain ("Dignity. Always dignity")
Blazing Saddles

And like David, about a zillion others ;-)