I can honestly say that I've watched all of them, except The Godfather trilogy. I chose Indiana Jones because it made Harrison Ford look much more awesome than the other characters in the other movie trilogies.
Lord of the Rings was epic, but hurt my butt for sitting those 3-hours-per-film. Not to mention it wasn't really all that fun to watch.
Pirates of the Caribbean was cool at first, but it kind of lost something as it went on. The relationship between Jack Sparrow and Elizabeth after the first film was something they could probably have done without.
Spider-Man was fun to watch, and loved the cameos made by the Evil Dead crew. ;P Too bad Venom was a let down. sad I was hoping for Carnage to make a brief appearance in the movie because of Venom, too.
Terminator and The Matrix... Well, Terminator 3 brought back Arnold as T200, but the movie's story kind of brought the trilogy to an unexpected climax. Which kind of sucked... And The Matrix was cool for the first movie, but the next two didn't really live up to the first film's fame. Possibly from all the full CG fight scenes.
Star Wars was awesome, but the first 3 episodes didn't really connect with the last 3 episodes too well. It would have probably been better if they left the coming of Anakin as some kind of prequel to Episode 1. That may have left Episodes 1-3 develop in better succession as 4-6 was able to do.
Back to the Future was going to be my pick, but as much as I loved the story and direction of the trilogy, it couldn't beat out the iconic silhouette of Indiana Jones. Plus, Indiana Jones dealt with myths and legends and came up with some awesome mysteries that lead the way to the discoveries. All of this and it includes a main character that is witty, respectful, chivalrous, and have the guts to fight against the Nazis, escape capture, disguise himself as a Nazi officer, then get an autograph straight from Adolf Hitler. blaugh