Kyle: So, I didn't get much time to defend why Back to the Future is the best. So here are the arguments that I couldn't spit out because Chris shut me down.
First off, Back to the Future as a trilogy does exactly what a film trilogy should: it establishes a world and its rules, presents scenarios that test those rules, and then it gives us the unforeseen consequences of when those rules are broken. While Star Wars establishes worlds, certainly, the fight between good and evil and all the events that fall into place are very telegraphed. Essentially it is a series of inevitable events and logical conclusions to the premises initially given. Indiana Jones, meanwhile, is hardly a connected world with established rules and premises. The first is (in subtext) about Indy's beliefs and commitments. The second is about his responsibilities to the world he explores, and the third is about what made him what he is. They are three largely unconnected stories about the same larger-than-life character.
My next point: Back to the Future had continuity like you read about. A small moment in the first or second movie pays off by the end of the series, no problem. You have Marty's accident with the Rolls Royce, Doc's mentions of sports bets in the first movie (paid off in the second), his mention of the old West and exploring the mystery of women (paid off in the third), Marty going insane when being called chicken, etc. Indiana Jones has very little in the way of continuity. Hell, we were given the three stories out of order. Raiders of the Lost Ark takes place in 1936, Temple of Doom takes place in 1935, and The Last Crusade takes place in 1938. By the way, after the whole "Ark explodes my private island" thing, shouldn't Hitler know who Jones is and recognize him in Berlin in the third?
Star Wars does a little better. At least it's in order. Of course, it's Episode IV through VI, but let's overlook that. There are still some continuity gaffs and obvious plot points that weren't thought through as well. I mean, Leia and Luke kissing twice before finding out it's incestuous, the effects of a lightsaber wound (blood? No blood? vanish? ah, who gives a crap), etc. You have to watch 24 and How I Met Your Mother back to back for several years to see such a difference in bad continuity and good continuity.
And also, Back to the Future shows us the progression of characters through years, decades, even generations. Star Wars shows us Luke's progression from farm boy to mystic warrior, Han goes from shameless pirate to responsible general. Other than that, there isn't a ton of progression from anyone else. Leia stays largely the same; Vader makes a snap change in the last fifteen minutes of the series. There isn't a continuous change.
Indiana Jones never really changes. He remains cynical, noble, intelligent, and defiant through all four movies. Even though he has experiences with different women, different sidekicks, and different villains, the song remains the same.
I guess it's all in the eye of the beholder, but if I had to sit and watch a trilogy in a single sitting, I'd pick Back to the Future over the others.