When did miniature use for tabletop games become almost mandatory?
The obvious answer is D&D 3e, when positioning on a square grid during combat determined what abilities and feats your characters could use. But I think a movement toward using miniatures had been building in the hobby for sometime before this.
The 1990s seemed to be a transition period for miniatures and gaming. Sculpts, in my mind, started getting much better than what had gone before (comparing my figs to my older brother's).
When I started playing D&D in 1989, I didn't have any miniatures. And it worked fine--I didn't have many players in my games either for awhile, just 2-3. We used the old standby, our imaginations for combat encounters. But when the number of my players grew, something had to be used to keep track of combat. Imagination is a wonderful thing, but 6 people around a tabletop can imagine some very different things during a combat.
Dice and coins worked for awhile. Then I started using figures from the boardgames HeroQuest, Battlemasters, and Warhammer Quest.
Even so, I mainly used them for the players to determine their character's place within the party's formation. I suspect this is the way a lot of groups used their miniatures. AD&D 1e and 2e were kind of vague on how to use miniatures (yeah, those measurements in inches in 1e kinda threw me off a bit--does an inch mean 10 feet or 10 yards?). I just didn't want to deal with it.
I also didn't like having to reach over my DM's Screen to push miniatures around. So, unless I had a complicated encounter, I didn't place my monsters down all that often. And it worked just fine.
The neat thing about D&D and miniatures in the 1990s was that miniatures were just supplemental. They weren't required. You could collect them and used them, but the even the rules stated you didn't absolutely need them. (Heck, even the rules said that the rules themselves were optional).
I think we lost something, perhaps a bit out of imaginations when 3e came along and made miniatures almost mandatory. Sure, you could buck the system--but then it'd be difficult to account for, say, Attacks of Opportunity.
I swear, before 3e came out, I never heard: "Hey, did he move through my threatened square?"
"Threatened squares" and "Attacks of Opportunity" where real game changers in my mind; they took the game out of people's imaginations and down to the physical tabletop, for better for worse.