Firefox has been my browser of choice for a few years, now. It's much faster than IE and has UI that is simple and function. You can also install add-ons to improve your browsing experience. I'll give you a few examples of what I'm using:
WOT, aka "Web Of Trust" gives you ratings for the sites you visit. It's a good, fast way to see if a site is harmful or offensive, ect.
Adblock, you know those annoying ads you see everywhere? You don't see them with this install. Makes browsing much less of an eyesore.
DownThemAll!, this really is one of the best add-ons out there. It's a download manager, and a damn good one. It's very nice for say, image boards for example.
NoScript- saved my *** from a shock site or two. (it has other uses :P) What it does and disable Javascript on sites. And yes, you can enable/disable it on any site you wish.
I have more add-ons installed, but these are by far the most important/best ones I've used. You can also theme Firefox to look the way you want, if you're into that.