Yes, replacing wiring is a big deal. Replacing the outlets, while time-consuming is easy.
Take one off and see if you have a ground wire-or better, check near your service panels to see if your house is grounded. There would be either a thick bare copper wire going from a service panel to a copper bar hammered into the ground and/or a thick copper bare wire going to and clamped to a water pipe (it is typically visible, but if not, you may have to take the cover off of the panel to see if it is in there).
I would be less worried about the grounding being absent than I would be about old wires. Old (tube and knob-yikes) wires do not have the insulation that new wires have and that means if lots of electricity is going through, it could get hot. Now, don't freak out. If you haven't had a problem, more than likely, you won't. Just be aware of what you plug in and where. Kitchen appliances, and heaters pull a lot of juice. Figure out which fuses or breakers are for which circuits (keep in mind that lots of plugs could be on one circuit-turn off of a breaker or pull a fuse and see what goes off -use a tester or a lamp to see which plugs go off and go through all of them) and spread your biggest loads out over many breakers.
If you need a ground (say your stereo is buzzing-actually that could be a dimmer switch on the same circuit, try a different one), you could, like we have done, add a ground wire just for that plug. I can tell you how.
Don't worry too much. I am an electrician and my house is not grounded. Well, actually, if you have electricty working, you are technically grounded (well, bonded-sort of the same). The other ground is for extra, extra safety (and preferable, certainly). You do have fuses or breakers.
Two things to watch for-too much juice for old wires )easy to fix like I stated above), or loose wires causing sparks. When you take off a few outlets, you will see the workmanship (this problem not really a big deal, as a big spark will blow a fuse or trip the breaker). This is easy to fix, too-just tighten the wires. it is not a common problem.
I am happy to answer more questions-ask away.