Option 1: Do nothing. There's not a whole lot of devices you regularly use that have a ground - that's why they only have two prongs on their plug.
Truly dangerous-for-people grounding situations should be covered by a GFCI outlet, and that doesn't actually need a ground to do it's job. GFCIs work by monitoring the current going out the hot, and back in the neutral. If there's more than a trivial difference, the GFCI breaks the circuit. The outlet doesn't use the ground, other than connecting it to a ground wire.
However, doing nothing does mean anything plugged into a surge protector isn't protected. Surge protectors route the surge to the ground. So if the ground isn't wired up, the surge protector can't do it's job.
Option 2: Truly rewire the house.
This is your most thorough, and most expensive option. Run new wire to everything and get a real ground. But it will cost a lot, and require repainting most of the inside of your house - the electricians will have to punch holes in the walls to run the wires.
The pluses are you know the wiring is new and modern, and you can add enough outlets to comply with modern code (at least 1 plug per wall, no spacing between outlets larger than 12 feet. 3 feet in a kitchen). If you're using a lot of extension cords, this could be handy. You should also use this opportunity to upgrade to a 200-amp panel, and circuit breakers.
Option 3: Do it piecemeal.
You can ground an individual outlet to the plumbing, and can do that one-at-time. There's some technical reasons where this is less ideal than the 'rewire' scenario above, but it's a lot cheaper. (Google "Ground loop" if you want to read about it. It's not likely to be a problem, but it is possible.) This lets you handle the surge protector situation mentioned above.
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