Sites often behave differently in IE than in other web browsers, so having debugging tools for this platform is important.
The Developer Toolbar for Internet Explorer versions 6 and 7 primarily provides a view of the DOM tree for a web page. Elements can be located visually and modified on the fly with new CSS rules. It also provides other miscellaneous development aids, such as a ruler for measuring page elements: http://www.microsoft.com/downloads/details.aspx?FamilyID=e59c3964-672d-4511-bb3e-2d5e1db91038.
Internet Explorer 8 comes with a set of developer tools that is much improved over previous versions' Developer Toolbar. Somewhat resembling Firefox's Firebug extension, the Developer Tools suite provides a console for JavaScript execution and logging, as well as tabs for JavaScript debugging and profiling, and CSS and HTML inspection and modification.
Microsoft's free Visual Web Developer Express package can be used not only to build web pages, but also to inspect and debug JavaScript code: http://www.microsoft.com/express/vwd/.
To run the debugger interactively, follow the process outlined here: http://www.berniecode.com/blog/2007/03/08/how-to-debug-javascript-with-visual-web-developer-express/.
This free tool gathers an enormous amount of performance data for web applications and displays it in a number of ways for further analysis: http://ajax.dynatrace.com/pages/.
The DebugBar provides a DOM inspector as well as a JavaScript console for debugging. It is especially useful for Internet Explorer 6 and 7, which do not have their own consoles: http://www.debugbar.com/.
Memory leaks in JavaScript code can cause performance and stability issues for Internet Explorer. Drip helps to detect and isolate these memory issues: http://Sourceforge.net/projects/ieleak/.