Trying to fix JavaScript bugs is huge pain as is determining the styles applied to an element. Firebug makes these issues a lot easier when working on Firefox, but what do you do when the code works fine on Firefox but IE is complaining?
You can try Firebug Lite or use Visual Studio to debug the JavaScript.
you can also check out the IE Developer Toolbar which isn't a debugger but will help you analyze the contents of your code.
Visual Studio will help with the debugging
Fiddler should help analyse the traffic travelling to and from your browser
Have a look at DebugBar. License is free for personal use
The IE8 beta comes with what I think is the IE Developer toolbar, but it seems to be a lot more powerful than the last time I tried the toolbar on IE7
See also Javascript Troubleshooting Tools In IE, a similar question that was asked recently.
Wait -- How does one debug Javascript in Visual Studio? Is there a separate debugger for it? (I'm a VS newbie, so please- do tell!)
Firebug lite doesn't work too well for me. The Developer Toolbar just isn't good enough. There really is no great solution.
Visual Studio 2008 can do JavaScript debugging, you have to go to IE's Tools->Internet Options->Advanced and uncheck 'Disable Script Debugging (Internet Explorer)' in order for the browser to bubble up the errors it detects.
Once you're in Visual Studio you basically have it's entire debugging arsenal at your disposal. It's not as integrated as Firebug, but it is way better than anything we used to have.
For the DOM Inspector, try the Internet Explorer Developer Toolbar.
For the Net tab, try Fiddler.
For Javascript debugging, try Visual Web Developer 2008 Express Edition. (Or a higher edition of Visual Studio)
Also, try DebugBar.
I'm guessing this question was posted before the IE8 final came out, according tho some of the answers.
These days, IE8's inbuilt Developer Tools are great; and while the JS debugging isn't as useful as Visual Studio the Dev Tools in general much better than Firebug in my opinion. Between that and the Compatibility View Browser Mode I can handle all my IE6 development needs.