It really depends on what you are looking for in a browser. Internet Explorer has been around for ages, and has the full support of Microsoft behind it. It's got over 70% of the market share and as a result is recognisable to almost everybody. It is sleek and powerful, but on old(ish) computers that may slow you down a bit. Still, as the standard browser, you won't find many other negatives with it.
Internet Explorer 8: http://www.microsoft.com/windows/internet-explorer/default.aspx
Mozilla FireFox is a highly customizable browser. It has the advantage of being the one of only browsers that is compatible with all operating systems. New themes and gadgets are released every week, and this gives a personal feel to it when viewing websites. Although it slows the computer down, it isn't as bad as IE, though on a fast computer, you won't notice much of a difference between the two.
FireFox 3.0.7: http://www.mozilla.com/en-US/firefox/all.html
Other options available are Opera Browser. This browser offers very limited customization features (only a colour change in fact), but because of this gives very fast browsing. It was mainly developed for low memory computers, and is more of an "Internet Suite" than just a browser. It provides users with the tools and technology to perform a wide variety of internet related tasks like viewing web pages, searching the Internet, sending and receiving emails, conducting online chats, and even displaying the latest Widgets. It doesn't require as many resources as IE or FF, but it isn't very fun to browse in something that looks as out-of-date as it does.
Opera 9.64: http://www.opera.com/download/
The final major browser is Apple Safari. In my opinion it is the fastest of the 4 browser and my personal favourite. Its style is based on the iTunes layout and it doesn't offer any customizability, but if you like iTunes, you'll love this browser. Its major downfall is the fact that it doesn't render (load) webpages very well. This can become very irritating while browsing so most people don't give it a second thought. It has many of the same features as IE and Firefox, including: QuickTime multimedia technology, a tabbed-browsing interface system, and internet searching tools. It does run very fast (even on slow computers) and has the best startup time of all browsers. If you find that the pages you usually visit work fine on Safari, you won't have anything bad to say about it.
Safari 3.2.2: http://support.apple.com/downloads/Safari_3_2_2_for_Windows
A new introduction to the Browser market is Google Chrome, Google's first attempt at an internet browser. It is now out of beta mode and it seems to be one of the fastest browsers out there. It is still fairly new on the Browser market so extensive testing ahsn't been does, unlike IE or FireFox, yet it is already the main browser used by many professionals. It isn't customizable, but Google have announced that they intend to allow plugins like FireFox, so it won't be long until they have plenty of add-ons to keep us happy.
Google Chrome 2.0.167.0: http://www.majorgeeks.com/Google_Chrome_d6037.html
So it really depends on what kind of person you are and what type of computer you have. You can't go wrong with IE or FF, but under stress, they perform slowly, Opera is a boring looking browser but can run where the other two can't, Safari has problems with rendering many webpages and there are far too many security risks with Chrome, but is much the fastest of them all. I personally use four of them (don't really enjoy the experience with Opera) and have no problem with any of them, though IE 8 and Google Chrome are the two I use most.
Hope that helps~