There are currently (as of July 11, 2002) 19 unpatched security holes in Internet Explorer. What does this mean? Well, in short, it means your ass is totally vulnerable when using IE. Hope you've got some lube handy.
According to the same source...
As of this time, there aren't any known Mozilla vulnerabilities. Mozilla is available for almost every OS under the sun, including the Mac OS(es), and Windows.
Opera 6.01 and 6.02 both have holes (so go upgrade if you use it!).