There are a numerous sites that allow you to download scripts. Among the best are:

The daily script: http://www.dailyscript.com/
A decent collection of scripts.

Drew’s scriptorama: http://www.script-o-rama.com/oldindex.shtml More than just script downloading. Also has a selection of TV scripts, and an update section so you can see what has been added recently.

Screenplay 451: http://www.pumpkinsoft.de/screenplay451/
A small but worthwhile collection with a number of top quality movies. Doesn’t seem to be updated anymore.

Screenplays For You: http://sfy.ru/ One of the best collections – loads of movies, updated regularly, and a choice between Word (good for cutting and pasting) or PDF (easier to read).

Simply Scripts: http://www.simplyscripts.com/index.html
A great site. Not only an extensive collection of movie scripts, but also Treatments, Radio Scripts, Anime Scripts, TV Scripts, Unproduced Scripts, Plays, Musicals, Non-English Scripts, and Oscar Winners. Great links section too.

The Weekly Script: http://www.weeklyscript.com/?referer=sfy
Very easy on the eye – the movie listings give basic info about the film and even have a small image of the video/DVD cover. A good quantity of movies, and a handful of TV scripts also. The links section is also worth rummaging through.

More sites for downloading scripts...