Some folks at the Web Standards Project have put together a slick little website called BrowseHappy.com (very Carbon-ish design, if I may say) that highlights the four principle alternative browsers: Firefox, Mozilla, Apple Safari and Opera. I've used all of these but Safari, though I have used recent versions of its close cousin, Konqueror. I can say with confidence that all of them are superior to IE in almost every siginificant regard.
The one area where they're not superior, is in compatability with applications that rely on IE's idiosyncracies and proprietary extensions, like Outlook Netmail. (It's a Microsft application, what do you want?) But for many such applications, the "incompatabilities" can be resolved by simply setting the user agent string to let you masquerade as IE. (That's a standard feature on Opera and KHTML browsers like Safari and Konqueror, and an easy add-on for Mozilla and Firefox.)
I'm a Mozilla user. Since version 1.1 or so, I've used it for everything that didn't explicitly require Internet Explorer. In that time, it's gotten faster, smaller, more feature-packed, and developed better and better support for web standards. Intentionally or not, this site is optimal in Mozilla, since that's what I use when I'm building pages. IE compatability tweaks are the last step I take for my personal sites.
I'm also an enthusiastic booster of Mozilla Mail, which is baked into Mozilla. It's fast, standards-based, robust, secure, easy to learn, and provides some of the best support I've ever seen for multiple email identities. One big reason that I prefer Mozilla to Firefox is that Mozilla does come with the mail client baked in, and I'd have to go and get Mozilla Thunderbird to switch to Firefox. I have some general gripes about this arrangment, but overall, either Mozilla or Firefox+Thunderbird is a good, safe, usable combination.
The message: Go for it, folks. Switch to a safe browser. And while you're at it, switch to a safe email client, too.