As a homeowner, you can make modifications that don't comply with building codes; but you bear liability for anything that doesn't pass code. AFAIK, electrical code in my area requires outlet grounding be made only at the power panel.

Since my two prong outlets already don't pass code, I don't see how it would make a difference. Even though it's not my house, I'd consider paying for a rewire (long story cut short: I'm not a traditional renter, I live with family and don't mind making contributions to home improvement) but it's too expensive. I do plan on replacing all of the two prong outlets with GFCIs soon, but obviously the electronics workbench wouldn't benefit.

 

GFCI stands for GROUND FAULT which requires a ground. Perhaps you can run a heavy duty extension cord to a grounded outlet.

Did you check inside the existing boxes? The box may be grounded with armored wiring. If there is a wiring clamp holding the wires you could run the ground wire from the clamp screw to the new outlet. Home owners are allowed to replace switches and outlets.

 

GFCI stands for GROUND FAULT which requires a ground. Perhaps you can run a heavy duty extension cord to a grounded outlet.

Ground isn't required. But labeling each outlet protected this way with a "NO EQUIPMENT GROUND" sticker is.

Without a ground, the tools used by building inspectors won't work; because they require a ground connection. When they see the stickers, they know they need to press the test button on the GFCI.

EDIT: Add reference link.
http://ask-the-electrician.com/installing-a-gfci-outlet-without-a-ground-wire/

 

The use of GFCI sockets is a good idea, in conjunction with a couple of ground rods driven at least 6ft apart and bonded together, or hook up one using your water supply and use the test button to see if you have trip current.
Max.

 

Even though it's not my house, I'd consider paying for a rewire ...

How many circuits do you have in that basement room? (More than one?) Can you kill all the power in that room with one breaker?? If that is the case you could just run one wire. But if you are running one, you might as well add a second circuit unless the wiring path has space limitations. In an ideal world you would run new wire that includes a ground conductor for those circuits in that room. May not be possible in your case.

I do plan on replacing all of the two prong outlets with GFCIs soon, but obviously the electronics workbench wouldn't benefit.

Note that you only need ONE GFCI for each circuit - the first outlet in the wire. If wired correctly (to the "load terminals on the GFCI"), the rest of the outlets "downstream" can be just regular outlets protected by that first GFCI.

THE WHOLE POINT of bonding the earth to the ground pin on all the outlets and any building steel (including a workbench) and then the ground pin back to the nuetral at the panel is so that if there is ever a fault which connects equipment case to a hot wire, enough current will flow back through the ground bonding wire to pop the circuit breaker and shut down the circuit before anyone has a chance to touch something that is live.

If I put a ground rod out through the window and ground my workbench to it, I will have a nice safe ESD workbench, but I have created an unsafe workplace. If a tool has a fault and the case of the tool becomes live, I can touch the case of the tool and my workbench and kill myself with the current flowing out to the outside ground rod (only takes about 100-125 milliamps if I recall). Since there is no ground conductor connection back to the main panel neutral, the breaker may not trip - especially if the ground around the house has significant resistance. So please be sure you install those GFCI outlets before you install the ground rod. The GFCIs will trip if the current going out to a tool does not exactly match the current returning on the neutral and protect you just as well as if the circuit was grounded.

I had an older house like this in which all the upstairs wiring was ungrounded. There were two circuits going upstairs, so I ended up installing two GFCIs on the wall by the electrical panel and connecting those circuits to the load side of the GFCIs. You could do that too - put the GFCIs back at the panel and protect everything on those circuits. (Or use GFCI breakers - although they are pricey compared to outlets.)

A second issue is if you ever have lightning in the area. If I have a ground rod on one side of the house connected to the entrance panel, and a ground rod on the other side of the house connected to my workbench, there can be significant difference in potential between those two ground rods (read thousands of volts) if there is ever a lightning strike. That is why the NEC specifies one and only one grounding system for a house, at the entrance. (Imagine a lightning bolt at 1,000,000 volts striking the ground. Imagine ground resistance which creates a potential difference of 1000 volts for every foot away from the strike point. That is why cows get killed in the pasture - with front hooves 4 feet away from the rear hooves, standing across 4000 volts is not healthy...)