The rarest characters we've seen in the last decade are Prince Charming, Prince Phillip, Fairy Godmother, Evil Queen, Captain Hook, Mulan, the Cinderella mice, and Remy and Emile from Ratatouille (when the movie was in theaters). We've also seen on rare occassions different Star Wars characters in TL that aren't part of the SW show: Captain Rex and Boba Fett.
Not rare: We have seen Peter Pan, Wendy and Alice frequently, once playing follow the leader in FL. (Once we saw the whole cast of Alice in Wonderland riding King Arthur's carrousel.) Tweedle Dee and Dum appear frequently as do Mary Poppins and Bert.
Spotting any character is a thrill, especially rare ones. I'm still waiting for a chance to see Piglet. And I'll never forget the first time we saw Donald Duck back before he regularly appeared and when we saw Dopey at Epcot in WDW.
Have your camera handy at all times because some of the rare characters we've seen were walking and not stopping to pose for pics so we scooted ahead of them and snapped a photo of them in motion. They will smile and wave for the camera, but once they're walking, they don't stop.
Through you can't pose for pictures with them, the best bang for your character-spotting buck are the parades.
Also, cast members at the info booth near the hub are often in the know about who is showing up where.
Have fun!