Currently I have the two wires no ground wire and some two wire with ground outlets (upgrade some time before). Is it allowed in the NEC to run a separate ground wire from one of the two wire with ground outlet to the two wire outlet without changing the old wires?
It is acceptable to run a separate ground to each box, but like Rusty said, if the wiring to the boxes is BX (flexible metal) or conduit, and the boxes are metallic, then your chances are pretty good that they're already grounded. A GFCI isn't a cure all, and will only work if it has it's own ground. It must also be properly wired to protect downstream outlets.
better to spend eight dollars and replace it with a GFCI outlet. It will protect every outlet downstream of it if you can determine which one is first. use the labels on all protected outlets.
If your electric wiring is in conduit or BX the problem is easy. The metal casing is the ground. Just install three prong outlets. The mounting screw makes the connection. If you have (Romex), the plastic covered wire cable, you will have to attach the bare copper wire to the green ground screw.
It isn't allowed to ground the new 'grounding' receptacle to another receptacle on another circuit (if that is what you are asking) Other than that, it IS allowed to be grounded to an accessible point on the grounding electrode system (metal cold water pipe or wire connected to it), the system grounding electrode (ground rod, etc.), the ground bar in the panel from which that circuit originates, or the grounded conductor bar in the panel which the circuit originates (neutral bar). The only other legal option is to install a GFI and label it No Equipment Ground. You can connect downstream receptacles to that same GFI, but cannot connect a ground wire from the GFI to any downstream receptacles and they too must be marked No Equipment Ground and GFCI Protected. The way a GFI works is quite simple. If the current on the hot and neutral conductors isn't the same (within 5mA), it trips. So if there is a different path from hot to anything other than neutral, it will trip.
