When doing any form of web development, the end goal is always a smooth interface for a user. When making both the server-side code that generates a page or the frontend interface template, problems are sure to follow. Maybe an accidental typo in the JavaScript bricked the interface, or the small snippet of CSS went horribly wrong; whichever the case, a tool that can show the hierarcheal progression of HTML elements and their associated pieces of CSS and DOM code enable a faster approach to debugging since you will know which chunk of code is creating the problem.
When debugging, there are multiple tools that allow you to take a look under the hood of any web page. My personal favorites are the ones that integrate with browsers. Depending on which browser you use, your choice will vary. If you are using Internet Explorer, I suggest getting Firefox.
For the brave souls developing and debugging for Internet Explorer, Microsoft offers a toolbar with some tools that come as close to the Firefox or Opera debugging experience as you can find on Internet Explorer. The screenshots say everything that needs to be said.
Opera's Dragonfly, which is currently in an alpha stage of development, is a fairly robust tool that provides debugging tools for JavaScript, CSS and DOM inspection, and error detection. Although the Opera browser itself is not released under an Open Source license, the Dragonfly debugging tools are available under the BSD license. It is still a product in Alpha, and there are many features under development.
The second alpha release is the next step towards Opera Dragonfly 1.0. Look forward to new features such as DOM editing, improved JavaScript thread handling, XHR and HTTP monitoring, improved keyboard navigation, and translation into a number of languages in subsequent releases.
*Note: Dragonfly provides tools such as integrated validation in a single extension whilst Firefox requires two extensions for a similar functionality. A single extension provides a further integrated interface and cohesive sets of tools. This is hardly a drawback for choosing Firebug, but merely a slight benefit for Opera users.
Lastly, and most certainly not least, the excellent combination of Firebug and the Web Developer toolbar demonstrate the power of Firefox - its extensions. There really isn't much to say. Firebug provides the similar tool-set of CSS and DOM inspection paired with error detection. The web developer toolbar has many nifty tools such as a ruler for measuring pixels on a page and built in validation for external and local files.