In my area, the majority of electrical is run in EMT conduit. Conduit acts as the grounding wire.

Get an electrician in to check it. If there is no ground you really should either switch the outlets out for two prong outlets or install GFI outlets that can be used without a ground. It seems really unlikely, as grounding has been code for a long time and, if it's romex-like cable, finding it without a ground is hard and not much cheaper.

In some installations the boxes are grounded with the wire not necessarily visible. In our house I was able to pull the metal boxes, pull the ground wire inside the box and ground both the outlet and box per current codes (using bigger boxes that would meet the current fill requirements). This was a way easier fix than re-wiring!

If the grounding is through the conduit I'd test it at every outlet to ensure continuity. I suspect, but don't know, that code now wants a grounding wire directly to the receptacle rather than relying on the mounting screws.

I agree with the comments above. The easy way to check for ground without having to take off any receptacle plates is to get one of these inexpensive plug-in testers: Receptacle tester

Klein Tools makes good quality electrical test equipment.