I'd actually like to add an extra element to the question - we sometimes perceive ourselves differently than others perceive us so it would be interesting if people say what Muppets they think we remind them of. Maybe not everyone's willing to do that but i invite anyone who wants to to Muppet-analyze me. I don't mind doing things like that since it comes from decades of having an artistic mindset/mentality where i'm always self-analyzing what makes up identity...plus when an actor is reading a script and getting a sense of the character, i've wisely been taught that the best way to do so is to note how the character perceives himself and what other characters say about him so i guess this is an extention of that kind of character study i'm used to doing.
There's a few i identify with...
Gonzo - he's the weirdo among weirdos and i've always felt that - the outsider looking in - plus he's passionate about his art and loves stuff that most others don't completely understand. I've always had that artistic temperment of feeling like i'm more of an observer of life more than a direct particopant in it. He wears his heart on his sleeve, has severe emotional highs and lows...and has physical features that make him stand out and seem odd.
Which brings me to my other Muppet(s) i strongly identify with: Sweetums - though actually the Muppet Monsters in general. I've gone through various stages physically in my life - very cute kid to horribly awkward geeky looking tween/preteen period - then it was a total transformation from ugly duckling to swan as i has a very good looking teenager/early 20's (i'm not ashamed or too modest to admit that i was a total HAWT-ie) and then i think because i had experienced periods of extreme ugliness and extreme handsomeness and learned how very differently people get treated based on looks, part of me wanted to denounce that a bit and be taken more seriously by others so i started being less concerned with appearance and wasn't afraid to let myself by ugly or let myself go a little. Then around the end of my college years, i came to terms with my sexuality and started becoming a part of the gay community which is horribly looksist and someone who might be considered a "10" to the general public can often be made to feel like they're a "-2" in the gay community so at the same time i was renouncing the "pretty boy" parts of myself i was also re-experiencing the self-hatred and discrimination one experiences when they're not attractive. Then came the late 90's when i had a lot of bad things happen to me including and especially severe bronchitis destroying my singing ability for a number of years which propelled me into a deeper depression than i'd ever experienced before (and depression has been a lifelong battle that i fight to this day)...which resulted in a very sudden boom of a weight gain of 50 pounds which i've never been able to take off since (i've gone through stages of being in better shape and losing weight but i've never gotten to being back to "ideal weight") so i've always felt a strong identity with the Muppet Monsters as a result - i knew they were the coolest Muppets but other people were scared of them because of their looks. My favorite shirt of all time was one that had Sweetums on the front and "Tall dark and handsome" on the back. Sadly that shirt has worn with age and frequent wearings.
Cookie Monster - kind of an extension of everything expressed above in terms of how i relate to Muppet Monsters in general but also because i love cookies, have a voracious appetite (i've never smoked save for a week when i was 13 - and anytime i've had to smoke onstage for plays...it seemed for a while when i was around 20 i was always getting cast in parts that required me to smoke cigars, never done drugs ...unless you count over the counter diet pills... and very rarely drink and never to the point of getting drunk so food has always been my major vice especially since growing up i was one of those types who could eat a whole bunch and not gain weight...that pbviously eventually changed.) Cookie dough especially is a huge weakness/comfort food. Plus i have the same way with a one-liner and "Cookie Monster" was my nickname in college because of my Muppet love and cookie/food passion.
Fleet Scribbler - when i first got involved with forums, i would play around with different screennames - sometimes having a new one each week but i finally settled on Fleet because (a) he was one of my fave obscure Muppets - the guy made me laugh aloud every single time he made a rare appearance and (b) i wanted a name associated with a Muppet reporter but didn't want to go with The Newsman because it was too obvious and also didn't want to have things always falling on my head. But overtime i think i've come to relate to the guy in other ways such as wanting to know everything i can about the Muppets which is what his function was as a gossip columnist and also that whole thing of outsider looking in - feeling a part of but also sometimes removed from the community of Muppet fans. I'm not big on thread muffining or doing things like the dorms or stuff like that and i can sometimes be very forthright with opinions and when one takes strong stances and stands up for things, they also risk being disliked and being an easy target for others.
Johnny Fiama - even though we actually have little in common, i'm not Italian (though love the food), don't have a monkey bodyguard, and very different personality/temperments, i think just the fact that he's a Muppet singer (and one who's male unlike Miss Piggy) and one that's big on crooning (though i'm more apt to be influenced by people like Roy Orbison and Chris Isaak as opposed to Tony Bennett and Frank Sinatra).