Ann Romano pretty much takes the cake for me - Franklin's inept performance and limited skills molded a cheesy character into something monstrous, false and endlessly irritating. I suppose there's something weirdly appropriate about the cheesy Romano being grating.
And in the Hall of Shame, among adults, I'd also put Linda Lavin's Alice. And Maude in MAUDE was pretty damned irritating, all the time.
Among pseudo teens, Horshack in WELCOME BACK KOTTER.
And among all the creepy "cute and funny" child characters, Urkel in FAMILY MATTERS, the lisping idiot Cindy Brady in THE BRADY BUNCH and all the spin-offs, and Larry Mondello in LEAVE IT TO BEAVER.
Special award (points for anyone remembering him) goes to the execrable Crazy Guggenheim (Frank Fontaine) turning up on Jackie Gleason. Now THAT was irritating.