Ah, so many...
But if I had to pick just one, it'd be one that started as a throwaway secondary character* in a long 3e game, who rolled rather atrocious stats in comparison to the party average and whose basic concept (I later found out) wasn't very 3e-friendly at all: I tried to replicate a 1e Illusionist. (spec. Illusion, banned Evokation)
* - we were each allowed to play two at a time in the party through most of that campaign.
As she was something of a throwaway, and as her Wisdom was a mighty 7, I could legitimately get away with playing her as a complete airhead and thus I constantly had her doing all sorts of silly-yet-amusing things, expecting at any moment her career to crash to a halt either through the enemies killing her or through some self-inflicted disaster.
Incredibly, she survived...and survived, and survived; long after my so-called main character had bitten the dust and to the point where - after all the pre-existing party members had either died or retired - she became the senior member of the party!
We give out year-end awards across our various games for things like Play of the Year, Most Valuable Character, etc.; and every year she was played (2001-2007) she never came lower than second in the voting for Most Entertaining Character, winning it three times.
Her career ended when she was killed off by her own party after frying them (and the enemies) with a fireball from her self-built Rod of Wonder.
Appppil Pagey, I'd play you again in a heartbeat!