In my work, browser compatibility is critical. It's no longer "cool" to just put a link that says: "For optimum use, we recommend " and append "Microsoft's Internet Explorer", "Mozilla's Firefox browser", Opera, and/or Google's Chrome.
A carefully designed website has to work great on all the major browsers (Internet Explorer, Firefox, Chrome, Safari, and Opera) and be functional, at least, on the less known ones (see
Other Browsers). If your website doesn't, it's either a sign of laziness or just plain incompetency.
Thus, in my web arsenal, I have FF, IE, Chrome, Safari, and Opera. I usually test my website under FireFox first and then move on to the other browsers. True, it can be tedious to test a website's layout and functionality on so many browsers, but it has to be done.
One of the tools that has been available in FireFox has been
IE Tab,

an add-on that allows the web developer to view how a particular page will look like in IE. I have found this tool to be indispensable since I don't have to open IE itself.
Another add-on that has proven itself to be invaluable to the web developer is
Firebug.

What is nice about Firebug is that it integrates itself so well with Firefox to put a wealth of development tools at your fingertips while you develop your web page. You can edit, debug, and monitor CSS, HTML, and JavaScript live in any web page.
Of course, all the tools I mentioned above can only help so much. You still have to apply the right CSS (Cascading Style Sheets) to your webpages so that they will appear correct on every browser you're testing it with.
Cascading Style Sheets or CSS is an entirely huge topic and you might want to read up on it if you're not familiar. Facility with CSS is a must for any web developer and tools and guides abound in the Internet. One of the best sites to learn from is
Zen Garden.
At work, we have to contend with some clients who are still using Internet Explorer version 6. I don't have any clue as to why these users don't want to upgrade. According to a
Wikipedia entry, as of October 2008, 36.01% are still using
IE6. This is a reality that every web developer has to face.
Conditional comments comes to the rescue. They work as follows:
Conditional comments only work in Internet Explorer on Windows, and are thus excellently suited to give special instructions meant only for Internet Explorer on Windows. To learn more about them surf over to:
Quirksmode.
Hopefully, this blog post helps you. It's a continuing battle to develop websites that will work and look good on all browsers and versions.