No, you aren't responsible for the actions of whoever is driving behind you. However it is suicidal to not be aware of what is behind you, as motorcyclists in particular will attest. However, it is becoming less the case that the person rear ending another is automatically at fault.
Case in point: I drive an 18 wheeler. Its equipped with forward facing camera, accelerometers, a radar system ( Eaton VORAD) and fairly extensive datalogging. Don't blindly assume my 80,000 lb. vehicle can stop short if you decide to stop for a stale green, miss your turn or whatever. Unless I am driving like an ass, the data logged by my vehicle systems is admissible in proving I wasn't at fault.