Whether or not your operating system needs an anti-virus program, it is still possible for you to be tricked into visiting a faked web site and revealing your password. For example, I had a client who received an email asking him to confirm his BT password. The link in the email took him to an online spreadsheet crafted to look like an authentication page. He was fooled and had his email hacked as a result.
Some security software that runs on Windows will try to combat this by maintaining a database of 'bad' web sites and alerting you if you attempt to visit one. At best this can only ever offer a partial and incomplete defence against such fraud. I don't know if there is a Linux equivalent.
