The best free anti-virus software out there are either "AVG" or "Avast", both have a good record for detecting viruses, on many online surveys.
I have tried both programs, and I found Avast to be the better of the two packages, it has a cleaner interface, and performs many additional functions that it appears AVG does not (like analysing and recording important systems files on your computer, allowing you to recover them should a virus destroy them).
Unfortunately you HAVE to be connected to the internet in order to update ANY antivirus software, there is no other way to do it.
To rebut some previous answers...Norton isn't free (apart from a 30 day trial, after which you have to pay) and is very resource hungry, thus slowing down your computer; Spybot, Adware and Windows Defender are anti-adware/Malware programs, not antivirus programs, but Spybot and Adware are good programs to have on your computer (but only if you connect to the internet).
If you're not connected to the internet, then you are only going to get a virus if you get files on disk from an infected machine, which would be quite rare, and any anti-virus software you did install from whatever site would always been a few months behind on virus definitions...but much better than nothing.
As long as you have a basic firewall (Windows XP firewall after Service Pack 2), antivirus (Avast), anti-spyware (Spybot and Ad-Aware SE are very good), and keep your copy of Windows up to date then the internet is a safe place (just don't open up attachments your weren't expecting from people, and scan things you do download before opening)...I've been connected to the internet for 8 years and have never fallen victim to a virus (only encountered 2 and my antivirus software squashed both instantly before they had a chance to do anything).