Coming out of lurking mode... Being a reader of the forum since around 2009, I hoped to get in on this, but I wasn't sure if my low post count would disqualify me. But Scott said it didn't matter if you were a lurker or a regular poster, as long as you're a game show fan, your vote was welcome. So, thanks Scott, both for undertaking this project, and for letting us lurkers contribute!
I tried to base my definition of "greatest" on a combination of factors--quality (both of the game and production), impact/influence (both on game shows and pop culture as a whole), longevity, and "fun factor" (including play-along ability, and simply how fun I felt the show was to watch). I took the approach of tiering my selections. I thought my top 20 or so were pretty solid, but after that it became a bit more of a crapshoot. In the end, though, I actually ended up with about a dozen extra shows that I wanted to include but simply didn't have spots for.
I suspect that my list turned out to be pretty in line with the consensus, although there may be a couple of oddballs (though I think they're defensible).
Looking forward to sharing and seeing everyone's lists and thoughts.