You can simply replace the existing outlets with GFCI outlets and receive some of the shock protection offered by grounding an outlet. You can get replacement GFCI outlets for around $10 each, so you should be able to replace the commonly used outlets fairly inexpensively.
You want to explain that one in electrical engineering terms?
A ground fault is when current, instead of taking the neutral line, is flowing over the ground conductor. On a standard 120V North American outlet, you've got hot (+/- 120VRMS), neutral (0V - bonded to ground at the head end), and ground. Normal current flow is on the hot and neutral conductors, with nothing on the ground conductor.
In the event of a ground fault (insulation failure, water, etc), you'll have current flowing on the ground line. A GFCI detects this current through the ground connection (they're pretty sensitive - typically 10-20mA is enough to trip one) and trips, cutting power to the hot line. So now you've just got neutral and ground connected, and no hot line run through.
If you don't have the ground conductor run to the outlet (the ground is disconnected), then you will
never have current on the ground conductor. Even if you short hot to ground, there won't be any current on the ground conductor, because there's nowhere for it to go. It's not connected, so outside the rather minute capacitance of the screw, it's got nothing.
At least, this is my understanding of the mechanics of a ground fault outlet. You seem to have a different understanding. Care to expand on it? Because my knowledge of a ground fault outlet is that, without a connected ground, it won't ever do anything, and is therefore worse than nothing (because it costs more, and offers a false sense of security that it can't deliver).
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OP: 120V tingles an awful lot, but as long as you're running fairly new appliances in the outlets, it's unlikely to be a major problem. If the cost to replace the wiring with a ground exceeds your current budget, then replace the outlets with two prong outlets. It's better to not have the ground pin on a non-grounded outlet than to have one, plug in something that is designed assuming the ground is valid, and then have trouble. Anything that only has a two conductor cord should be designed such that it doesn't require a ground in the first place.