They’re not my favorites, but I haven’t seen them mentioned yet so I thought I’d give a shout out to Andy and Randy Pig (from the too-short-lived Muppets Tonight), who referred to guest star Sandra Bullock as “Sandra Buttocks,” and who wiggled and waved their arms around uncontrollably during a panel discussion on Arms Control.
Twiddlebugs.
Dear God, I am old.
Guess!
Blue. The Muppet in question was blue.
In fact, he was referred to on script as “Fat Blue.”
Now that’s what I come to the Straight Dope for. 
It doesn’t get any cooler than The Count.
In fact, one of my favorite “The Daily Show” bits involved The Count. During the Bush v. Gore recount fiasco Stewart said, “We’re going now to the world’s foremost expert on counting, Sesame Street’s Count.” Cut to the Count saying, “That’s one, one vote for Gore! Two, Two votes for Gore! Mwah, hah, hah!!”
As a kid, it was probably Cookie Monster, then Grover, then the Count. And I think I was into Oscar too. But I did have a Cookie Monster puppet.
When the “Muppet Show” happened, it was Animal. And I never got that Animal puppet I wanted, for which apparently I still carry a grudge. And Beaker. And Gonzo.
As an adult, looking back, it’s still Animal, followed by Gonzo (Gonzo seems to have more of an appeal to me as an adult than he did when I was a kid, though I don’t know why.)
Thanks, Askia.
Piddleypoop. If you’re old, then I’m old. And I just don’t see that happening.
Beaker
and the singing vegetables in The Muppet Christmas Carol if they count.
Miss Piggy! Maybe it’s an association thing, but I have to love a pig who knows what she wants and fights tooth and hoof for it.
Plus, I’m sorry, that scene where she ties up Josh Charles in Muppets in Space? HOT!
It’s Animal for me!
“No, no Animal, BEAT drums, not *EAT * drums!”