Excruciating, agonizing, racking mean intensely and, usually, unbearably painful. All are commonly used as strong intensives and applied to pain, suffering, and torture. When used to qualify other things, they mean causing intense pain or suffering.
Excruciating carries strong suggestions of acute physical torture or of exquisitely painful sensation.
Agonizing stresses anguish of mind even when it strongly implies physical suffering.
Racking suggests sensations of pulling and straining and tearing comparable to those suffered by a person on the rack.