Recommending Norton is like recommending a punch in the face.
All AV programs have viruses they do not detect (right now, anyways). Same with anti-spyware software... Such is the way of the malware war. For the truly paranoid, there are several good online AV scanners offered, which you can run periodically. Panda Software's, Trend Micro's, etc. Definitely a bad idea to install multiple AV programs due to definition interference (especially Norton and anything else).
Norton is far, far worse because Symantec does not provide any scanning engine updates with the subscriptions, rendering you vulnerable to every new class of virus. They only provide definition updates to detect the classes of viruses the engine knew how to detect when you bought it. You have to keep rebuying the software every year, which is usually pricier than a subscription...
"Once I had a PC that had 6 different viruses on him and Norton with latest updates didn't see any of them. Not a single one. "
My guess is that it was not the latest Norton AV.