Can I replace an outlet that uses knob and tube wiring with a grounded outlet? Obviously the best choice would be to replace the old wiring. Is there a standard way to ground these outlets? Do I need to run a wire back to the circuit breaker box? Do I have even the slightest idea of what I'm trying to ask?
If you need a receptacle that can accept a grounded plug but don't actually have a need for grounding, you have two options: (1) a GFCI-type receptacle marked with the words “No equipment ground,” and (2) a three-prong outlet protected by an upstream GFCI and marked with the words “GFCI protected” and “No equipment ground”. See section 210-7(d)(3) of the National Electrical Code.
If you actually need grounding, I'm afraid there are no shortcuts: you will have to rewire. A trick to avoid opening the walls is to run the new wire in the (unfinished) basement or attic, then drill up from the basement or down from the attic into the wall where you want the receptacle. Try to be a little more careful than the previous owner or electrician who rewired our house: we have a couple of holes in the floor because someone missed the wall! If you rewire, you may have to obey the code's requirements for number and placement of receptacles, not sure. In our house, the old two-prong outlets in the baseboards have been disconnected and left in place.
Per code, you have to have a separate ground wire if you have a grounded outlet. Replacing the old wiring is the best, but it's a big job. Removing all the old wiring would require you to open up a lot of your walls because the wires will be secured at multiple spots with knobs, and you may have splices at unexpected places that prevent you from pulling the wires through.
I assume that if you have knob & tube that you also have lath-and-plaster walls? Depending on how your house is set up, you may be able to take some shortcuts and still be legal. For example, if you have an unfinished basement, you could feed a loop of wire up through a wall cavity to a receptacle (probably in an old-work box): one side of the loop goes toward the service panel, the other goes to another similarly wired receptacle. That way, you can daisy-chain several receptacles in a room without damaging the walls too much.
Are you asking if it's OK to run a separate ground wire from the existing? The answer is no; all your wires have to be in the same conduit (see also this question) and any rework of existing wiring has to be done to current code.