According to a confirmation by Microsoft late last night, a new zero day vulnerability has been found to affect every version of Internet Explorer. In other words—over a quarter of the entire browser market.
It's pretty clear to me that security vulnerabilities will never cease to exist. There will always be some backdoor, some new exploit the dev's haven't patched yet. It's a question of who has the wits and resources to uncover them, and of their intents and relationship with the dev's.
You can prove a program, which can help in assurances of security. http://stackoverflow.com/questions/476959/why-cant-programs-be-proven From a cursory search, I found this as an example of a formerly verified web browser: http://goto.ucsd.edu/quark/. I don't happen to know a lot about this approach (I know nothing about this approach, really), but I do know that you can make certain guarantees about security (I guess assuming there are no bugs in your implementation of what you've proven).