This old house is (50's) is wired with cloth covered 12/2 Romex with no ground and all metal boxes. Can I just run a 12 ga or 14 ga solid wire between boxes and then to the ground bus of my service panel or do I have to replace all the wiring with new Romex?
I believe that it MAY be code-accepted to retrofit a grounding conductor as you describe. It would need to follow the same path as the existing wire. Check with your LOCAL electrical inspector before taking that on faith, though. Depending just how ungrounded your system is, you may also need to install a ground rod (or two, or three) so that your service panel ground bus is actually tied to ground.
Considering what will have to be done to retrofit this wire, I believe that the sensible approach is new wiring (if you were going to rip things that far apart), or GFCI's and the old wiring with code-approved labeling noting the lack of ground on those circuits (if you were not going to rip things that far apart).