Hot Scripts is THE definitive source for free scripts on the web. Here you'll find literally thousands of free as well as paid scripts. Find scripts by programming language and rate scripts based on how much you like them. You can also read reviews from previous users.
Free-Scripts.Net - Free mIRC and CGI scripts, webhosting, html guide, email checker, chat, and many other things. I'm not sure how much this site is updated, as the last news entry was from 2003.
Java File is a site that offers over 600 free Java scripts to use on your web site. The scripts are organized by easy-to-navigate categories. There's probably a free script for just about anything you want to do with your website.