TNG used it plenty of times as well. Maybe more than TOS. Q, the overseer of the Edo, the dowd, Nagilum. Probably others I'm forgetting, or don't exactly fall into that category, but still use the trope. The guardian of t'kon comes to mind. While not a "god", he certainly falls under the "all powerful mind reading wise and enlightened ancient alien" trope, basically the same thing.
DS9 was all about a godlike race, the Pah-wraiths. The founders were treated as gods by the dominion. I'm only on the third season so far, but that's two already.
I didn't watch Voyager because it was such obvious crap, but I'm pretty sure the caretaker qualifies...
Seems like later trek series used it just as much.