Do you know any shows that have changed the order in which the cast is credited signiffigantly? I mean like, more than 3 cast names were rearranged over time.
I know Home improvement did this alot!

Seasons One, Two, and Three Order
Tim Allen
Patricia Richardson
Earl Hindman
Taran Noah Smith
Jonathan Taylor Thomas
Zachary Ty Bryan
Richard Karn (Only credited in seasons 2 & 3)


Seasons Four, Five, and Six Order
Tim Allen
Patricia Richardson
Earl Hindman
Jonathan Taylor Thomas
Zachary Ty Bryan
Taran Noah Smith
Richard Karn

Season Seven Order
Tim Allen
Patricia Richardson
Earl Hindman
Richard Karn
Debbe Dunning
Zachary Ty Bryan
Taran Noah Smith
AND Jonathan Taylor Thomas

Season Eight Order
Tim Allen
Patricia Richardson
Earl Hindman
Debbe Dunning
Taran Noah Smith
WITH Zachary Ty Bryan
AND Richard Karn

I think a lot of Soap Operas from the 1980s to today really do this practice

Even though One Life to Live in their 1984-91 intro doesn't list the cast members' names in the openings, they definitely switched around a lot of the cast members' face shots and cast orders if you watch the intros from over the time period between 1984 and '91 really closely.

Others:
Probably Cheers and/or M*A*S*H had slight sequence changes w/ the cast orderings.