Q1: I heard that there was a member of the Rolling Stones who was loyal to his wife and never screwed groupies. Who was that?
Q2: And were there/are there any other rock stars who simply never indulged?
Q3: And I read a Morissey interview in which he said that just because you’re famous that doesn’t mean that anyone wants to sleep with you. Is it a myth that you can always screw something if you’re a rock star?!
Q1. Charlie Watts
Bill Wyman also confirms this in his book, Stone Alone.
Q2. Sure. Some people are faithful to their wives, rock stars or no.
Q3. I don’t believe it for a minute. Unless you’re a drummer or bassist. 
I haven’t read Bill Wyman’s book in years, but I recall that he actually kept a running count of how many women each of the Stones had slept with. He claimed that Brian Jones had scored with more women than anyone else, with Wyman a close second, and Jagger and Richards coming up the rear. But Wyman had a zero by Watts’ name, because Charlie didn’t cheat on his wife.
So, were those big numbers–hundreds? thousands?
Q3: And I read a Morissey interview in which he said that just because you’re famous that doesn’t mean that anyone wants to sleep with you. Is it a myth that you can always screw something if you’re a rock star?!
Drummers always get the best lookin’ chicks (no offense intended to those who date other musicians). It’s the bass players who suffer.
Calling MythBusters!
(So which cast member gets put into a band to test this myth? The nerdiest? The ugliest? Hmm…)
Could be Kari, except that wouldn’t prove the point. 
Not Paul McCartney, I’ll bet.
I don’t have a cite, but I’d bet a dollar that Dee Snyder would fit on this list. In his testimony before the Senate, he revealed that he didn’t smoke nor drink and in interviews, he’s mentioned his long marriage to the same woman. He seems like a pretty clean-cut guy.
Alice Cooper, the most suburban rocker of all time.
I for one support this idea. 
I’ve heard that Queensryche, at least by about 10 years into their career as a major metal band, were considered really boring by bands they toured with, because they didn’t try to party after shows. Of course, that may have come with a little age.
I don’t think U2 is known for sexual escapades with groupies.
No good cite, but I saw an interview once where someone said that Bachman Turner Overdrive was one of the most boring bands offstage. The interviewee said that they didn’t drink or smoke and that all of them were married and didn’t cheat, so all that they did after shows was go out and eat.
That may have been their former bandmate from the Guess Who, Burton Cummings. Apparently the Bachman brothers are Mormons.
I’m gonna hazard a guess that the guys in Rush haven’t spent time with groupies. Alex Lifeson has been with the same woman since he was 15 years old; Geddy Lee has been married to the same woman since the early ‘70s; Neil Peart doesn’t seem like the cheatin’ kind.
And Geddy (I think) once mentioned that starting out their career by traveling with Aerosmith and KISS taught them how not to behave on the road
Brian May of Queen was apparently not a partier. According to that page, he avoided drugs or alcohol, was a nonsmoker, and was not sexually promiscuous.
Do the Barenaked Ladies and They Might Be Giants have groupies?
I’ve heard that the BeeGees still do. Six groupies, IIRC, that they meet up with after concerts for drinks.
I worked security at a TMBG concert, & they didn’t even sign autographs. It’s like they get all of their extroversive tendencies out on stage, then turn back into introverts immediately.
I hung out with BNL backstage at a show - mostly before the show. Ed Robertson was a very nice guy - easy to talk with; we spent about an hour together just hanging out. I got NO sense whatsoever that they partied or did the groupie thing - at all.