I generally shoot dance now at around 1/125 or 1/160, higher for really fast sequences of intense movement (flips or what have you) and those do generally freeze enough of the movement if your timing and camera movements are correct too - except as you say a swinging hand or foot but they're only a little blurred by the motion. ISO varies but I'm often shooting smaller stages and dimly lit pieces rather than big, bright, open productions.
I think each individual sport will have its own demands and 1/125 may be enough to freeze enough of the motion of the player but if you're shooting with a 500mm lens (for example) then there will probably be some motion from the photographer/camera that needs freezing as well. Panning shots of players or animals or cars in motion, 1/125 is probably enough with the right technique and for some, plenty ... it also depends what you're trying to achieve, and the lighting conditions that the sport is in will affect the aperture and the ISO. I'm not really sure what the question is ...