I definitely watched the first two or three seasons obsessively. I had a massive crush on Ten Danson as Sam Malone. (He'd also been super hot in the Aramis commercials) and Diane was a character I related to, but HATED relating to. I was (am) an intellectual snob with literary pretensions. So I hated being a Diane, but there it was. I was very caught up in the idea of Sam and Diane getting together and I still think that scene IS one of the hottest things ever. (I couldn't find a Youtube clip, but I'm sure you know the one I mean.)
However, as we all know Sam and Diane (along with Dave and Maddie) are the classic examples of "They Did It" as a cause of Jumping The Shark. In Sam & Diane's case, it is definitely true. I think the problem is that what clearly happens between them in the scene is hate!sex and there was no way a mainstream sitcom in 1983 was going to base a relationship around that. So instead we had the ridiculous back and forth where they were supposed to be in love, but were just too different, instead of just saying they hated each other's guts but wanted to fuck all the time.
I never bought into any of the crap with Diane and Frasier and I didn't like Woody as a replacement for Coach. What had been fun about Cliff and Norm started getting on my nerves. Since was a Diane and Carla was all the bullies from High School, I didn't like Carla or feel sorry for her. I NEVER took to the Rebecca character, so I was pretty much over the show before Diane's departure, but I think I remember watching that episode and the way Sam said "have a good life" was kind of heart breaking.
I didn't bother watching much after I came to SF in 1986, but I may have seen episodes here and there and I definitely watched the last one. At the time, I thought it was a total bummer, but in retrospect it gets better and makes more sense.
My Sam/Diane shipping was so great that I used to name stuffed animals and "original" fic characters after them, but I had no interest in Shelly Long besides Cheers and my Ted Danson interest didn't really last past his appearance in Cousins where I was so actively rooting for William Peterson's character (who was a bastard) and found Ted's to be an annoying wimp.
I never bothered to watch anything else he was in and certainly didn't give a damn about him coming onto Cheers as the 2nd replacedment for (HAHAH) William Peterson. Strangely enough I do find him hot in Something About Amelia. It definitely says something for his personal charm that he was able to do that part while Cheers was still on the air and not have his career suffer for it.
So my final analysis of Cheers is that it only worked for me as a "single ship" program. While the ship was there, I was devoted and once the ship was gone, I had no reason to watch.
However---when people ask me about the Mint, I have been known to tell them that it's my "Cheers."