In Mortal Kombat 9 (2011 version) for the PS3 and Xbox 360, each character has multiple fatalities that they can perform at the end of the match.
This is the list of all finishers (two fatalities, one babality, and one stage fatality) for Quan Chi.
All of these moves can be unlocked and added to your moves list by performing them in either Arcade Mode or Versus Mode.
Check out these complete fatality guides for more finishing moves:
Fatalities and babalities for Mortal Kombat on PS3
Fatalities and babalities for Mortal Kombat on Xbox 360
Quan Chi’s Fatalities & Finishing Moves
Xbox 360
Beat Down — Forward, Forward, Down, Down, X within sweeping distance
On Your Knees — Down, Forward, Down, Forward, B within sweeping distance
Babality — Forward, Down, Back, Y in jumping distance
Stage Fatality — Back, Forward, Down, Y at close range
PS3
Beat Down — Forward, Forward, Down, Down, Square within sweeping distance
On Your Knees — Down, Forward, Down, Forward, Circle within sweeping distance
Babality — Forward, Down, Back, Triangle in jumping distance
Stage Fatality — Back, Forward, Down, Triangle at close range