For those who don't believe that an ordinary commercial VPN service can improve your privacy, here's a simple experiment you can run at home: Get two similar computers, one with a VPN and one without. Use them both to download Hollywood movies through bittorrent, and see which one results in notifications of incoming lawsuits from movie studios.
Fortunately, there's no need to do this experiment yourself. Millions of people around the world have already done it for you.