Fats was important because he brought pool into peoples houses and conversations and on TV(and no I'm not compairing myself to him, I will never be 4% of what he was). But he did make pool a household thing at least for me growing up in the 70's, older and younger people might have a different view. I'm also answereing this question as in a one person influence right now, so I cant say Diamond(Greg/Mark). I'll get to that later.
If I was going to say a company, Brunswick is important because they have been around since the Civil War, Diamond is huge these days, But I bet Sears sold aot of pool tables from their catalogs for many years thus bringing pool into peoples houses so thats different than pool hall pool, they might have sold more tables than Diamond has(Yet).
The movies Hustler and COM both helped alot, COM made Bushka a bigger name than he was before the movie, Gus Szamboti in pool rooms has been a big name for years, for people who know that their eyes light up when you show them a Szam or Bushka-more so than any other cue makers(not a knock either), Brunswick made a pile of cues too, getting cues in the hands of alot of people, so did the "Fat's" cues at K-Mart(I think thats right sears had someone as well) again my point being bringing pool to the masses.
Pat Flemming captured alot of recent history for a established niche market, which is cool but I dont think he brought many people into pool rather he served a market he didnt create a market(not a knock). I'm trying to answere this in a broad sence, "who put pool infront of the most people in recent history?"
Those are some of the influential people and companys that got us to where we are today reguarding pool as a home game, not as a proffessional sport or league thing, tournment game etc., from my perspective as a 41 year old person. Someone old like Jay might think greenleaf did more

.
the real question for a different thread is who is gonna do more in the future....