I have an older home, built in the late 50’s. The majority of the outlets have been replaced with 3 prong outlets over the years. I have not checked every out let, but the majority of them are ungrounded. I wanted to see 1) how dangerous this is and 2) short of rewiring the entire house, what are the possible solutions (installing GFI outlet, etc.)? Any thoughts or suggestions are appreciated, thanks!

What type of wiring, Romex or armored cable? Are the boxes metal or plastic?

Romex... the original boxes are metal, thanks.

Simplest option is to find the main power lead coming into a room and insert a GFCI as the first outlet. Then connect all other wires in the room to the "load" side. Use the "No equipment ground" labels. If you have a rancher on a basement, you can probably rewire fairly easily. 250 ft. 14/2 romex is on Amazon with free shipping for $55.

Thanks for your response. I have a 3 story, so rewiring would be quite difficult/expensive.

I just want to confirm my understanding of what you said above, if I replace the first outlet on each undergrounded circuit with a GFCI outlet (and mark each as no equip. ground), I should be in-line with code and good to go?

GFCI's can be used in place of ungrounded receptacles AND used for those ungrounded receptacles down line on the same branch circuit. All receptacles must be labeled GFCI protected with No equipment ground.

In a house of your vintage, if you have an old panel, the neutral and service ground are on the same bar. The neutral conductor is bonded to the grounding electrode both at the service supplying the circuit as well as at the secondary of the transformer supplying that service. So in a round about way you do have a ground although not dedicated.
New installs have separate ground and neutral.

New NEC requires AFCI in many rooms now but they do not work for ground fault and I don't believe they can be downstream loaded.

You can buy the GFCI's in boxes of 6 at HD and Lowe's and save money. Good Luck.

Thanks for all your input! Now I just need to determine which outlets are first one each circuit.