How about Wolfenstein:Enemy Territory? Old but fun. It used to have a mod named True Combat:Elite that was a counterstrike clone which was very much fun as well, but that seems to have vanished.

I also loved the old Delta Force series and I have heard good things about the ARMA series. However, I am not sure how much ARMA will work without Steam.

Insurgency : Sandstorm

I think it requires steam but iirc there are community servers so maybe there are non-vac servers (which shouldn't require steam)