Indy is the only ride where certain effects might be working differently each time you ride.
However, there are still tons of other rides that give you different experiences every time you ride based on:
1) Interactiveness- Buzz, Mad Tea Party, Roger Rabbit, and Toy Story Midway Mania rides are each different because you have control over the ride. In BLAB and TSMM you aim at different targets. In MTP and RR, you spin your vehicle, which changes the experience each time.
2) Where you sit in the vehicle- Any of the roller coasters are different in the front, than in the middle, than in the back (BTMRR, Screamin, Space, Matterhorn, etc.). Some rides give a better ride in the front; others in the back. Depends on the ride. Also for Grizzly River Run, you can never tell which seats are going to get the most wet. That ride changes everytime based on where you sit.
3) There's so much to see that everytime you ride you see something new- I'm thinking like Pirates, Haunted Mansion, any of the dark rides, Nemo, It's a Small World. While the actual scenery/ effects don't change ride by ride, there might be things that you didn't notice the first time around or if certain effects are set to a timer, you might not have seen them before on previous rides.
4) Cast member interactiveness- I'm mostly thinking of Jungle Cruise and how each ride is different based on the CM skipper telling the jokes. But this can also apply to the Main Street Vehicles, Turtle Talk w/ Crush, or Monster's Inc./Toy Story Midway Mania with their respective interactive audio-animatronics that PP talked about.
Indy is a combination of these 3 as well as certain things that change every ride like audio, pyro, ride movement or special effects.