While I always test my site with several browsers to ensure compatibility, I have really developed an unhealthy infatuation with Mozilla Firefox. I really like this browser.
It seems infinitely extensible. I've already discovered a great many features I never knew I needed and extensions (plugins) galore. It does amazing things such as correctly rendering standards-compliant pages. And it's not vulnerable to all of the standard IE and Windows security holes which, because of their tight integration, normally lend themselves to significant and numerous opportunities for compromise. I will note that Firefox has its own security issues; see this for some examples. It's still a much better browser even with the holes (maybe the developers are just trying to keep up with IE in this regard).
One of the most important things about using a browser other than IE is that I get to see many web pages precisely as the developer intended, including my own. For instance, IE does not always render the sidebar correctly on my site. Take a look at the Random Thought archive for September 2005. Even though the page is valid XHTML and CSS, IE often places the sidebar menus at the very bottom of the page. I assure you that is not how it's designed. Another example of bad rendering under IE is the comments area on any post. When there are comments (see this post for an example), IE loses track of the various shading areas and carries arbitrary colors across the page under the posted comments. It's nothing more than a drawing problem since scrolling the page up and down will either change the colors or correct it (you don't have to refresh the page for IE to change the colors, just scroll past the comments area then back to see what happens).
Firefox too has its own rendering issues, but they are far less obtrusive than those in IE, and at least Firefox accurately renders most web standards.
Some of the very cool things about Firefox (and other browsers such as Opera, but not IE) is the tabbed browsing motif. When I'm working on a post with references to other sites and/or stories, I keep those pages open until I'm done writing my entry. This gives me speedy access to the reference material I need. This can sometimes mean I have six or more pages up at the same time. Using the tabbed interface of Firefox, I only have one browser window open. This helps reduce desktop clutter.
I won't promote a single browser because I think the options available are diverse and support a great many surfing habits and preferences. That's why I only keep a link on the front page to the Browse Happy site. As long as you have a standards-compliant browser, I'm happy — since my site is strictly compliant and needs that compatibility to render properly. Which browser you choose is up to you and based on what you need and how you like to work.
I do recommend, however, that you not use IE. It's too problematic, too incompatible with standards, and too proprietary in its treatment of content (even between versions; I have to hide certain CSS elements from the Windows version of IE but keep them available for the MAC version — how pathetic is that?). Oh, and it's one of the biggest security threats installed on your Windows-based computer — secondary only to the operating system itself.
Head over to Browse Happy and get a real web browser today. You'll be glad you did.