If you were to ask me, I'd say that the following rides aren't going anywhere:
Magic Kingdom
Space Mountain - too iconic
Carousel of Progress - Walt himself said it should never cease operation so there would be a huge outcry from the Disney faithful. Not worth it.
Tea cups - too iconic
Dumbo - too iconic
It's a Small World - World's Fair, iconic, Walt designed... it's not going anywhere.
Haunted Mansion - way too iconic
Hall of the Presidents - Walt helped design, it's patriotic like Walt which leads me to think he would have been against tearing it down, Like Great Moments with Mr. Lincoln in
Disneyland which will never be removed.
Pirates of the Caribbean - too iconic to go anywhere.
Jungle Cruise - too iconic to go.
Epcot
Spaceship Earth
Hollywood Studios
Great Movie Ride - just because it is in the replica of the Chinese Theater. They aren't going to want to tear that down and they need rides in the park. Great Movie Ride is really a ride that represents what Hollywood Studios is. Unless they completely change the theme of the park, I don't see it going anywhere.
Animal Kingdom
I don't think anything is 100% safe. Maybe the safari and Everest.
Great Movie Ride is my favorite in Hollywood Studios, so I could be projecting. Who knows. I don't think anything is safe in Epcot except for Spaceship Earth. Maelstrom is my favorite and I don't think it is very safe. Splash Mountain is my favorite in Magic Kingdom and it is wildly popular, but since it is based on Song of the South, I can see them getting rid of it at some point if there is enough public outcry. Jungle Cruise is high up there for me, as well.