Is there something like "Firebug for IE" (for debugging 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

Since Internet Explorer 8, IE has been shipping with a built-in tool-set for debugging, troubleshooting, and generally helping in development of your pages/applications. You can access these tools by pressing F12 while in the browser.

HTML Tab

The HTML tab will let you peek into the DOM as the browser understands it. As you select elements from the HTML view, their styles will be detailed on the right, with individual rules have the ability to be toggled on and off. You can also modify rules, and determine whether the styles on the element were inherited, or assigned explicitly. Additionally, you can even tell which .css file they originate from.

There is a bit more you can do in the HTML tab, such as review and modify attributes on elements, and even make changes to the layout of the element from within the layout section. Additionally, you can make changes directly to the markup to quickly test out some structural ideas.

Script Tab

For resolving JavaScript issues, you can watch the Console and the Script Tag. If your script stumbles across an a call to an undefined method, you'll be alerted within your console. The console also lets you run arbitrary JavaScript against your page, if you want to toggle items on or off, or try bind a handler to a button.

The Script tab great as well as it will format your JavaScript for you, allow you to insert breakpoints, step in and over code blocks, and watch variables over time.

If you've used Firebug, or even the Webkit Inspector, the F12 Developer Tools in Internet Explorer 8+ should be pretty familiar to you.

You can try Firebug Lite or use Visual Studio to debug the JavaScript.

Firebug lite doesn't work too well for me. The Developer Toolbar just isn't good enough. There really is no great solution.