Most people knew basically one type of web browser when I was growing up: Microsoft's Internet Explorer. I used it for years until about 2 years ago when I finally switched to Firefox. Firefox, the current version being 3.5.3, has several advantages over Microsoft's IE. It is generally regarded as being more stable, meaning it does not crash as often or have as many exploits. One of the reasons why I eventually changed to FF is because IE would randomly crash while I was using it. A window would pop up, relay an error code, and then shut down my browser. It started to happen so often that I became frustrated. In the time that I have used Firefox, I have never had as many frequent disruptions, although to be fair, I have experienced a few.
Firefox also provides many options for add-ons, which are third-party developed features. I have installed a few of them and find them to be very helpful. Most of the things I install are safety features that protect me while I peruse the internet; for example, I use WOT, or Web of Trust, which provides safety ratings of the websites that show up in my search engine. Other add-ons fall into several categories, such as features for music and videos, newsfeeds, etc. I have not seen any kind of support for Internet Explorer of this magnitude.
Firefox is updated frequently as well, which demonstrates that the developers are constantly working to improve it. Recently, a version of Firefox conflicted with another program I regularly use, Steam. The problems were relatively minor, such as having Steam's menu show up on the left side of my screen randomly. A later version of Firefox remedied this oddity.
The download size of Firefox is relatively small (around 8MB), so there is not a huge risk in installing it since it will not consume many resources. Switching to Firefox is generally painless as well because it can import your bookmarks from Internet Explorer (if you use it).
Alternatives to Firefox do exist though. I have tried other browsers like Opera, which seems to be a worthy competitor to FF. Some people prefer browsers like Safari, although I do not have a Macintosh, so I cannot really comment on its performance. It is best to experiment with several to see which one is right for you.