None of the Analog Read Examples are working with 2560

Have you tried replacing

  int sensorValue = analogRead(A0);

with

  int sensorValue = analogRead(0);

I don't have a Mega to hand to test what A0 compiles to (its definitely done different in Arduino 1.0 from earlier Arduino softwares - I can't find the definitions in 1.0). Perhaps its broken for Megas? Sounds a bit unlikely though.