By the way, i’m not really deep in internet security but i believe that with just browsing web pages – without downloading any suspicious files – you won’t get infected with viruses.
Unfortunately there are attack vectors exploiting your browser flaws to run arbitrary commands on your computer just by visiting a webpage. (that’s why people should always have their browser up to date)
There are various annual hacking contests just for that where computer security researchers get rewarded for their findings. For example, the Pwn2Own contest ( http://en.wikipedia.org/wiki/Pwn2Own ).