I’ll try to be brief but to anyone new, here are the broad differences in a nutshell:
Shown to test audiences in 70mm. Lacks the narration, happy ending, unicorn dream and most of Vangelis’s score. Lots of alternate takes (some used by The Final Cut); a curiosity piece.
The Theatrical Cut:
Shown to U.S. audiences in the cinema in June 1982. Uses a voiceover narration and happy ending.
The International Cut:
Shown to international audiences, this was also the version released to home video and ended up in The Criterion Collection. Near identical to the U.S. Theatrical Cut, but adds additional shots of violence.
The Director’s Cut:
Released theatrically and later released on home video. The first version to be released on DVD in 1997 and the only one until December of 2007. The first version to removes the voiceover narration and happy ending and adds the unicorn, but uses the U.S. Theatrical Cut as a base, meaning no additional violence.
The Final Cut:
Released on DVD, Blu-ray and HD-DVD in 2007. Removes the narration and happy ending, uses the additional violence from The International Cut, extends the unicorn dream sequence, uses alternate dialogue and additional shots, fixes continuity errors and erases wires with CG. Uses remixed 6-track high def audio and radically different colour timing compared to the previous versions.
And that’s just what’s commercially available from Warner Home Video. The CBS Broadcast Version and The San Diego Sneak Preview are so obscure, I doubt I’ll ever see them.
So if you find Blade Runner out in the wild, chances are it’ll be The Final Cut, but don’t let that be the end-all-be-all. No version is perfect, which is why fan-edits are so popular with this movie. The Collector’s Edition basically lets you construct your own personal Favourite Cut.
That information can be found in a billion different places around the web. I hope that was a copy and paste job and you didn’t waste your time typing it…