PB Blaster, nothing else is as good, soak it in PB Blaster then do some tapping and banging like Ken suggested.
Heat, well if you heat up the shaft and make it expand it might pop loose but for that to really work you would have to keep the key cool, not easily done.
The halfmoon or Woodruff keys are usually softer metal than the shafts, IIRC, so you can use a sharp center punch and punch a divot on say four spots, then drill into the key itself, this might let the key shrink in size a bit and it might come out.
Great chance to use a TIG welder, just zap the key with the TIG a bit and the key and only the key will heat up a lot, then put some water on it to cool quickly (only the key will get hot, you won't heat up the shaft so the quick cooling will NOT damage the shaft) the big swings in temp should make it break loose.
Another approach is to put the shaft in the vice, bearing end down, close the vice until it is almost gripping the shaft, the one end of the key should now rest on the top of the inboard vice jaw, then with a sharp cold chisel tap on the top of the key, the part than is NOT sitting on the vice, this too could break the key loose. I'd wrap the shaft with a couple of layers of tape just to keep from damaging it if the key comes loose suddenly and the shaft drops.
Keep at it, it will come loose!
The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.
William Arthur Ward