This is actually a tough topic for me. I don't really do old war-stories from my RPG sessions very well. I don't remember a lot of details about old characters. Usually my favorite character is my current character (and since my current game isn't D&D, well... Also, I GM a fair bit.) And my favorite characters aren't often D&D characters. I had a character that I envisioned as Bertie Wooster once, in a Call of Cthulhu campaign. He went insane when meeting with Nyarlathotep, who was incognito. I had a character who was a changeling rogue in an Age of Worms campaign. I envisioned him as a fantasy Don Juan, who had gone a bit too far--when discovered in flagrente delicto with a crime boss's wife (or mistress, I can't remember anymore) he found himself on the run. Because he was a changeling, he disguised hiimself as a young female barkeep in a small town outside of Greyhawk city; the little town of Diamond Lake where the adventure path was started was where he was in hiding.
I kinda liked the notion of a classic, Some Like It Hot vibe to the character. Sadly, although my DM promised me that that would come up, it didn't. He forgot, and my origin was so much wasted effort. In addition, I wasn't really a trapfinding D&D style rogue; I was more of a con-man and huckster. I found myself constantly pushed to develop in ways that were stereotypical for the class, but not really what I had in mind for the character.
I really liked that character. At about 10th level, I retired him, though, because the campaign just wasn't working in a way that allowed him to be who I wanted him to be.
My current character is, kinda sorta, in house-ruled D&D, but the Star Wars setting, set sometime shortly after Return of the Jedi but ignoring pretty much everything from the EU (if you accept a few things, like Clone Wars to be somewhere "above" EU in canon, more like the movies themselves, for instance.) He's a former Sith Acolyte who was disillusioned (and, in fact, majorly pissed off) at the Sith Order, and therefore came to the Jedi Enclave on... uh... whatever planet it was on when we started the game. (Dantooine. It's on Dantooine. Maybe.) He's not exactly "good"--in fact, he's not even close to being good. But he's interesting. But maybe the Jedi class isn't exactly D&D as most people know and love it. But my last two or three D&D experiences as a player ended up being a little bit disappointing in terms of my own character. And I don't really have any stories from "ye olde days." So, I guess that's the best answer I can provide...