Userscripts are a powerful way to enhance and personalize your browsing experience and also help in some specific debugging purposes (without the power of the Fiddler, but much easier to use).
The implemention of the idea started off in 2004 as an extension to Firefox browser and caught on really well. As of 2013, Greasemonkey is the 4th most installed ever Firefox extension (giving way only to such stars as AdBlock Plus and Firebug) – with over 2 millions of downloads, and over thousands of userscripts available for one-click installation. Along the way, other browsers (Opera, Chrome) have implemented limited built-in support for userscripts and Tampermonkey project was created to offer a fully equivalent extension for Chrome.
If all that sounds interesting, you may have a look at the presentation on userscripts that I performed recently during our in-house Web Talks session, and see the sample GitHub assistant userscript that adds some code-review capabilities to GitHub on-the-fly while you browse the page.