It should be noted in the doomed Air France 447 flight, the plane activated the stall warning because of a high angle of attack that was leading to stall. (thanks pdx for the corrected info) At some point the system rejected the data and stopped the stall warning because the angle of attack was so severe that it considered the data erroneous. This is speculated to have caused the co-pilot to keep pulling back on the…
AF447 was an Airbus 330 which does not have a physical stick shaker. It has a "Stall Stall Stall" warning that sounds and was likely drowned out by the other alarms that were filling the cockpit. A330s also have disconnected sticks, so when a pilot has input on one side of the plane, that input is not replicated on the other side of the plane.
Just to be clear, an Airbus 330 won't let the pilot maintain an attitude that could lead to a stall, so it has a much higher degree of protection than a simple stick shaker. The situations in which these protections are turned off are situations in which a stick shaker would also fail to function reliably.