Simply stated, you really need to ground your outlets, all of them. 3-prong receptacles require 3 separate wires; the black (or red) hot wire, the white neutral wire, and, what is usually a bare wire for the ground. This ground wire is probably what you‚Äôre missing, and although some later remodels in your home show signs of a remodel, they need to be checked to see what they are hooked up to. You can go to any hardware store and buy a circuit tester. It looks like a 3-prong plug on one end, and has some lights on the other. When plugging into a 3-prong receptacle, it lights up, and the combination of lights will tell you if the proper grounding is present. Of course, it will only plug into a 3-prong outlet.
Most houses built after world war II and before 1960 were wired with plastic-insulated wires wrapped in some type of sheathing. This is similar to modern cabling, except they only had 2 wires (black and white), and houses built since then (more or less after 1962) now carry the extra bare ground wire in the sheathing. This ground wire should tie every outlet box, receptacle, switch, or otherwise, to the main circuit panel , and then on to a grounding rod or water pipe . The safety aspect only works if they (the outlets) are all grounded to each other, and to the main circuit panel.
If these pre-1960‚Äôs homes were built using steel conduit or armored cable, it is possible that the municipality would allow you to use this steel sheathing as the ground providing it all leads back to the main circuit panel. Otherwise, a grounding wire needs to be added, and municipalities may not allow just a bare wire running exposed in all the walls. Adding GFCI‚Äôs adds a level of protection, but GFCI‚Äôs only protect items plugged into them. They can‚Äôt easily protect lighting fixtures or light switches, and many items found in the home could cause the GFCI‚Äôs to trip just by turning the item on. The ground wire is designed to help protect everything, inside and out. As an esthetic bonus, the grounding of the outlets helps cut down static in TV and stereo reception.
It is also unclear exactly what you have for wires in the wall. 1948 is a fairly transitional year, and, depending on type and condition, replacement may be in order. As a work-around, there are GFCI units that install within the breaker panel itself. Depending on what you have, this may be a viable, albeit expensive option. If you have a fuse panel instead of circuit breakers, this is really not an option unless you replace the main panel. Rewiring an entire house can be pricey, but much of the cost is just for running wire, and that can be a DIY project. If you decide you need to do it, shop around. You may find an electrician that would be willing to work with you on that.
A friend pointed out to me, that unless there are local amendments to the contrary, the NEC allows for grounding of outlets via a separate grounding conductor as long as it is installed so as to be "protected" and is properly connected to the house's grounding electrode system. This can be considerably less expensive than rewiring because you would only have to run a single wire to the outlets for a ground.
In closing, I should point out that both GFCI‚Äôs and a properly grounded house are necessary to maximize the protection to both the homeowner and home. GFCI‚Äôs are an extension to safety system the grounding wire provides, not a replacement.
There are so many different scenarios that could exist, but lacking the opportunity of a personal visit, the best advice anyone can give to those in these types of situations, is to seek out the skills of a qualified professional who can come to the property, ascertain the circumstance, and make a recommendation. You don‚Äôt need to use them for the work, but it will give you an idea on what needs to be done.
Good luck - TomR