Greasemonkey is a browser extension for Mozilla Firefox which can run so called userscripts that can change elements and information on websites in real-time. Some prime examples include link checkers, removing elements on a website or embedding price comparison information on shopping pages.
Microsoft's Internet Explorer on the other hand has seen some efforts in the past to include Greasemonkey support but most tries (Greasemonkey for IE, IE7 PRO..) fell short of delivering compatibility with the vast resources that the Greasemonkey repository at Userscripts.org offered.
The Internet Explorer plugin that came closest to supporting userscripts was Trixie. Trixie has not been updated in the last three years but it still works surprisingly well. There are however a few restrictions in place that make some scripts incompatible with Internet Explorer; This unfortunately means a trial and error approach to test if a script is working.
The only reliable method would be to install the script and see if it does what it says. Trixie requires the Microsoft .net Framework. It adds an entry in the Tools menu of Internet Explorer after installation which can be used to activate and deactivate scripts.
Scripts have to be downloaded and moved into the Trixie home directory on the hard drive. All scripts need to be placed in the scripts subdirectory of Trixie. Internet Explorer has to be restarted before the newly added script will be displayed in the Tools menu.
Update: Trixie is no longer available, the website where it was offered on has been removed and is now returning a server not found error message. Even worse, I'm not aware of any comparable solution for Microsoft's Internet Explorer. If you want to use userscripts, your best bet is to use a browser such as Opera, Firefox or Google Chrome.