I recall the Bambi rabbits were out at Disney Animal Kingdom to help promote the release of Bambi on Blu Ray. It doesn't seem that long ago but perhaps it was. Thumper and . . . Miss Bunny? I can't recall if she had a different name than that.
Again, it seems that not so long ago Jungle Book character King Louie was making appearances in Adventureland. Balloo comes out for appearances with King Louie at the Animal Kingdom park during the Disney Marathon - always a fun time to encounter rare characters, if the running doesn't kill you first.
Robin Hood has always been associated with the Magic Kingdom to me because characters from his movie (Robin Hood, Friar Tuck, Sheriff of Nottingham) were out and are captured in my parents' photos from 1970s trips and we have photos with Robin Hood from a family trip around 2005-06, and then he suddenly disappeared. I felt fortunate to catch the opportunity for a photo with Robin Hood, Little John, Sheriff of Nottingham and Prince John at Epcot during the half marathon in 2009. No Friar Tuck in that photo, poor neglected guy. ha-
Maybe after that, the issue becomes one of continuity? There are characters people expect to see on every trip and there are characters known to be in the parades. After those slots are filled who knows how the decision is made which characters to trot out on which days. I've never seen a guest survey asking me which characters my family wants to see but it is always fun when someone unexpected pops up like Pinocchio or Jiminy Cricket by City Hall.