Interestingly, I had to dig into my memory for this one. These days I don't have a lot of characters (and many of them haven't done anything noteworthy yet.) But back when I was in college, I had a bunch of characters such as Xylena Darkhope (human binder, D&D 3.5), Vrahn Targaryen, First of his Name (This was before the shows, okay? Lich wizard, D&D 3.5), and El Mariachi (Silver Ladder Acanthus, NWOD: Mage.)
But my favorite character from back then will always be Kruzko the bard. He is a half-orc bard that I only initially built because I rolled an 18 for the first time ever and thought it would be fun to have a half orc with max charisma (18 - 2 = 16.) So he's green, he has tusks, but he has aaaaabs. And biceps. And a lean, human body that makes sense for someone with Strength 16 and Con 14. (It was a really good roll.)
I've always found Kruzko to be interesting, because while he was the most outlandish character that I have done at the time, I found that he is the closest to my "true self" out of all of them. He loved life, he was charming yet off (half-orc), and when he found a goal to focus on he stuck to it even if it was sometimes no longer practical. In every edition of D&D since, I always looked at whether or not the new edition could rebuild him somehow. This was how much I liked the character.
(Incidentally, last year my friend +Rocky Sunico had an interesting talk about playing your true self. While it is my opinion that this is not always the case, it is an interesting thought piece nonetheless. Kruzko certainly was me, in a sense.)
Anyway, of Kruzko's many antics, my favorite was when we bypassed the need for a rogue in one of our adventures. In the keep that we were murderhobo-ing, we came upon a spiral staircase that was quite obviously a trap gauntlet. Back in 3.5 (correct me if I'm wrong,) only rogues can find magical traps above DC 20. So the party began to painstakingly tap individual steps with a ten foot pole, as careful adventures are wont to do.
"KRUZKO BORED!" He said. (I also had a class starting in 30 minutes and I didn't want to spend all of it looking for traps.) Kruzko then ran through the steps, triggered every trap, made all his saves for half damage, and then got to the top. "Kruzko thinks there is a trap there, there, there, there, there, and there." He then cast Cure Serious Wounds on himself.