Enter Logan 5, the focal character of Logan's Run, as you may have guessed. He's what's know as a "Sandman", a government agent whose job is to catch and kill "Runners" - people attempting to escape the "Carrousel" rebirth ceremony. Turning 30 himself proves to be quite the test of Logan's faith in the whole concept of "Carrousel", and the hunter becomes the hunted as he, himself, becomes a "Runner". This could very well have greatly inspired Minority Report, as the same feeling of the dangerousness of the running enforcer play a central theme in each of these movies.
From a special effects standpoint, Logan's Run really shows its age, but it also provides an interesting look at what Sci-Fi looked like before George Lucas introduced Star Wars and changed Sci-Fi movies forever. It is interesting to note that Logan's Run actually won a Special Achievement Academy Award? for special effects and was the first movie to use laser holography.
As an interesting side-note, Farrah Fawcett-Majors starred as Holly-13 in Logan's Run before she became popular. As a result, she's in the movie, but has a small part. Still, watch for her.
In short, the production quality is not anywhere near the big-buck sci-fi movies of late, but Logan's Run provides an interesting story and serves as a nice example of classic science fiction. If you can get over the pre-computer graphics special effects, the Buck Rogers hairstyles and the less than award-winning acting, Logan's Run can be a fun flick to watch. If not, it's excellent for hosting your own MST3K party.