Who's fault is it if you crack open your car door and a bicycle hits it?

The cyclist should have been being more careful, along with the motorist.

-- ANSWER --

Probably yours. If the cyclist was coming from behind and the bicycle didn't hit the back of the car then it would not have hit the door if it had stayed shut. If the cyclist was coming from the front, and didn't hit the front of the car then it would not have hit the door, if it had not been opened.

(I'm a cyclist, and I'm presuming that the cyclist was capable of maintaining a generally straight line.)

If the cyclist had to swerve out of his path to avoid another person or vehicle and hit you, then it might have been either the cyclist, or the other person/vehicle, which was At Fault.

If, however, you just didn't check for oncoming traffic, then it is totally your fault.

You say "you crack your door open" - just how far open was it?