Microsoft has improved the security of Internet Explorer with IE 7, particularly on Windows Vista where User Access Control blocks silent attacks. Sandi Hardmeier maintains a nice website on IE7 and the upcoming IE8.
All of these browsers are freeware now, in fact I don't know of a browser that isn't. :-)
Firefox has emerged from the ashes of Netscape as the safer alternative to Internet Explorer. It's other advantages -- tabbed browsing, faster page loading, popup blocking and ad blocking -- make it the browser of choice for most people who try it.
I'm an enthuiastic supporter of Firefox because it is driving standardization and extension of the Web, and because the large selection of add-ons for Firefox makes it versatile, fun and powerful. The success of Firefox also forced Microsoft to begin to respect website standards instead of using their favorite proprietary lockin tricks. That has been a prime Mozilla objective. ;-)
There are other good browsers too: Opera is comparable to Firefox, but it's usage is not as wide as Firefox's. Google is making a move to force web innovation with their new Chrome browser. It has some nice interface and browsing innovations, but is not yet as secure as Firefox or even Internet Explorer.
"OffByOne" is a small browser that actually fits on a floppy disk. It's also much quicker than any mainstream browser. Some sites may not be displayed exactly as intended, but most are good enough. I use it when I want to investigate a site or link that I'm dubious about. It's safe to use for unknown sites because it won't activate malicious content.
I've learned there is no point in writing about something before you look on the Web. I often find something better than I would have written. I found a nice article on browsers that is informative and easy to read. About.com has several nice tutorials [another] on how to get more from your browser. No point in me writing a lot more here about browsers in general.