Browser security is a huge issue, and according to many it will only become more of an issue. In fact, Trend Micro has state that within the next year, malicious websites and insecure browsers will be a bigger issue than the current king of compromise, email viruses:

"By 2008, most of the threats you are facing will be Web placed. Today most of it is still e-mail," Raimund Genes, Trend Micro's chief researcher, said in a presentation at the Gartner Symposium and ITxpo here on Monday.
While most AV suites today provide on-demand scanning for email, letting the system check them even before your mail program gets to retrieve them, the same is not true for web browsers. Should it pan out this way, how well a browser can protect you from outside threats will become just as crucial as having an up to date system is today. Many solutions exist, such as web proxy services and other content filters, but even those can often be lacking. We'll probably see a huge increase in what the standard AV suite does for this. Indeed, just about every month for a long time IE has been patched in one way or another, and that trend will probably continue with IE7. Firefox and other browsers are no exception, with security updates being the most prominent changes from release to release.