From experience, backstabbers do what they do because they are threatened. They see their targets as "threats" to their career aspirations and power base. As you do your job well, expect these people around you to start gossiping and find holes to dig deeper into in order to undermine your work and your personality. But don't let 'em.
And so when the "long knives come out into the workplace, the attacker must be confronted". Confront the "snake" and do it publicly. Be brave. These kind of people act the way they do because they are actually weak and insecure, so let them have it by exposing their deeds into the light and let the public see them for who they really are. More importantly, in doing so, you let them know who you are - someone they can't tear apart or put down. Trust me. I learned all this from experience.
A piece of advice to backstabbers out there, some of whom might even be reading my blog because they are still so insecure (hehehe) --- Don't ever hold the delusion that one's advancement can be achieved by crushing others.
In the end those who truly make it are the one's who really has something to offer, something more than the lies and rumors you spread about the others.