mecurtin has a good point below about plausibility and logic. That's one of the things I enjoy too - what changed in the past to result in this John or this Rodney or this Elizabeth? And I think that's another reason the stories that are totally removed Atlantis have to work harder to earn my interest. Rachel Sabotini's AU with John as spare nobility given in an alliance marriage to Rodney is a good example. For me, I absolutely believed that John-as-nobility would act that way, and that Rodney-as-researcher would act that way.

My problem with some AUs is that I really do suspect that the only connection the John/Rodney/Teyla/Ford have to canon is name and appearance. And then I don't want to waste my time with the story, because why bother if it doesn't have anything to do with the show?