My favorite Muppet Show character is always Gonzo.
Close seconds are Scooter, Beauregard, Janice, Zoot and Rowlf. It's hard to pick just one.
My least favorite Muppet Show character is Miss Mousey.
Let me explain this a little bit. Her Froggy Went a Courtin' bit with Kermit in the Valentine's pilot is priceless, but they never really developed the character beyond that. Her wardrobe alone didn't really match the rest of the characters. That would have been fine if they'd at least made note of that in the writing. She was used as an "available" puppet "at hand" when they needed a filler. There are more interesting Muppet fillers than Miss Mousey. Although her Don't Sugar Me bit with Statler and Waldorf was really good. Nonetheless, when asked - she's my least favorite Muppet Show character.
Runners up include just various whatnots I didn't particularly like placed here or there. I really do like the characters! If I had to pick one of the named cast that I didn't like - I mean had to - it would have to be Hilda because she never caught on with me like the others. I suppose underdeveloped characters are the ones I have the most problems with.