I do work with network security (that is, I monitor clients traffic on a network, looking for suspicious traffic) and I can tell you that Bittorrent is not the way people get virus/malware today. Neither is it via the network (a worm), and seldom via e-mail.
It is by visiting a website, which contains malware via Flash, Iframes and/or Ads. A so-called drive-by. This usually happens either by someone linking to a "dangerous" website in Facebook, Twitter or a public forum and saying it's a funny video of some kind. Or a popular website has gotten an Ad from a 3rd party where the Ad contains some dangerous Flash-code.
As long as you do not run the latest version of Firefox/IE/Adobe Flash/Adobe Acrobat Reader and you are at the wrong site at the wrong time, you get infected! And sometimes the latest version of that software is exploitable too.