Jimmy Neutron's Nicktoon Blast - you're joining Neutron & Carl on their mission to capture the Mark IV rocket from Ooblar. Explained in preshow.
Shrek 4D - Farquaad's back and he's going after Shrek & Fiona. Explained in preshow.
T2:3D - you're at Cyberdyne Systems to see their latest creation. Explained in preshow.
E.T. Adventure - you're helping E.T. get back to his home planet. Explained in preshow.
The Simpsons Ride - Sideshow Bob forces you and the Simpsons onto a not-so-stable ride at Krustyland. Explained in preshow.
Men In Black Alien Attack - you're going through MIB training. Explained in preshow (well, not really a preshow, but it gets the job done).
Jaws - you're taking a tour on Captain Jake's Amity Boat Tours. It's pretty self-explanatory, like the Jungle Cruise.
Disaster - you're helping Frank Kincaid and Disaster Studios out with filming for their latest disaster film. Explained in multiple preshows.
Revenge of the Mummy - you're on the set of the latest Mummy film which is apparently cursed. This one is a bit flawed as there's no room to get the story out of. The queue video monitors tell the story, but once you're in the tomb area you might not know what it's about. This is a bit iffy, and even I'll admit that.
Twister - shows how the film was created and all that. Explained in multiple preshows.
Incredible Hulk Coaster - I'll give you this one as I don't even know a whole lot about it's story. Basically I've never waited in the stand-by queue long enough to watch everything on the monitors. However, Wikipedia says "Volunteers enter the lab of Bruce Banner with many televisions showing the story of the Hulk. Bruce is now trying to find a way to reverse the effects, which the guests are about to take part in."
Storm Force Accelatron - Storm explains why you're on the ride before it begins.
Dr. Doom's Fearfall - Dr. Doom needs "fear juice" from riders in order to kill the Fantastic Four. Explained in preshow.
The Amazing Adventures of Spider-Man - you're at the Daily Bugle and will be testing their latest news reporting vehicle. No set preshow but the idea is picked up through video monitors and the highly-detailed queue.
Dudley Do-Right's and Popeye & Bluto's may not have preshows but they're no different than Splash Mountain in the fact that you're just going by scenes.
Jurassic Park River Adventure - river tour through Jurassic Park. No preshow but self-explanatory.
Dueling Dragons - STR8FAN2005 explained this one. Apparently the Potter re-theme of it will have a set preshow too.
Poseidon's Fury - you're touring the ancient ruins. Explained in preshow.
The Cat in the Hat - typical dark ride. No preshow necessary.