The most secure browser is still as weak as the operating system it runs on (or something like that).
All Web browsers are insecure to some degree, though, because they all must work with flawed code in the operating systems. There are some indications of progress, such as frequent patches from Microsoft and Mozilla to close security holes. Still, these actions may be too little too late if a zero-day exploit is the attack weapon.
I think you still have choices, as some browsers are more prone to hammering than others. Firefox doesn’t get it like IE, and Safari gets it even less. Still, some argue that certain browsers are simply built better. Anyone have an answer for that?