Yes, the lack of an equipment ground was common in older homes.
You have several choices. Install GFI receptacles at the start of each circuit and wire them so they protect the downstream receptacles, replace those receptacles with 3 prong receptacles and label all of them "GFI protected, no equipment ground."
Option #2, run an equipment ground from each receptacle back to the ground bus in the panel or to the ground wire from the panel to the ground rods or to the first 5 feet of metal water pipe in your house (if it is properly bonded to the panel), install ground fault outlet(s) and connect the ground wire you installed to each box using a green ground screw or a ground clip.
Option 3 (my personal choice) replace all the 2 wire cable in the entire receptacle circuit with a cable that contains a ground wire. This will need to be done all the way back to the fuse/breaker box. Install ground fault receptacles.
I really don't care for options 1 & 2. If it is at all possible to replace the wire, option 3 would be the safest & most reliable method (personal opinion).