Logan's Run is a pretty good movie. Very 70s-ish, but that's a plus in my book.
Basically it's a post-apocalyptic story. In the future, there's a complex where people live, but they are terminated at age 30 (or something like that - youngish) in a ceremony called the Renewal (or Time of Renewal or something like that. There's a trance song named that uses samples from the movie). Those that don't want to die, "run", but are chased down and killed by "Sandmen". Logan is one such Sandmen, but he is ordered by the complex's computer to become a runner to infiltrate a gang that helps runners. Thus the name of the movie.
IMHO, it's one of the bigger inspirations for the RPG "Paranoia"
Also a book, but the book is very very different from the movie, and not so great.
The Island is apparently very much like the movie The Clonus Horror (or something like that, a Mystery Science Theater 3000 movie)