Otto feels like a character that has verrrrrrry little relevance to the show in the wake of hair metal's demise, but is just another example of what could have been an absolute nothing side character (aka "the bus driver") being given a strong personality - in this case, a metal-obsessed burnout who's charged with the safety of children, despite not having a license or any form of identification beyond his underwear (when he's wearing his, that is).
Is that something a SPONGE would write?!
Recent Seasons Update: He had sex with Principal Skinner's mom during a Mardi Gras celebration.
Hank Scorpio is the best one-off character in Simpsons history (note: I haven't read the rest of this list, so the votes may disagree with me, but if they do, they are just wrong as hell). Albert Brooks lovingly voices this nice guy boss of Homer's, who also happens to be a megalomaniacal Bond villain. Between bombing France and threatening the UN, he's giving away moccassins and giving away the Broncos and has piles of loose sugar in his pockets for some reason.
Recent Seasons Update: Nothing really, since Scorpio was designed to be a one-off type character, but Russ Cargill (the villain in The Simpsons Movie) was pretty clearly originally intended to be Scorpio, right down to the Albert Brooks voicework.
For an absolute racial stereotype, it's hard to not love Apu (note to Indian readers everywhere: I know this character has caused you more annoyance than any fictional character ever). He ruins the local Quik-E-Mart in the most shameless manner possible (with brief interludes of others taking over, including actor James Woods) and has briefly changed his identity to Apu DeBeaumarchais (while with the Be-Sharps) and his parents to Herb and Judy Nahasapeemapetilon. By the way, even with all the Simpsons I've watched over the years, I still can't spell Nahasapeemapetilon without Googling it.
Recent Seasons Update: Apu cheated on his wife with someone named Annette, and his wife made him legally change his name to Slime Q. Slimedog.
Maggie, the eternal infant, the silent one, the...one who shot Mister Burns (spoiler?). Maggie's more of a prop than a character, but she's had some pretty great gags over the years - and is the impetus for The Simpsons arcade game (since removing a diamond from a child's mouth is way more difficult than kidnapping).
Recent Seasons Update: Still a baby. In the future, she marries Gerald (the unibrow baby) and they have a child of their own (who looks a lot like Maggie).
Springfield's resident mad scientist and Jerry Lewis knockoff, Professor Frink'll make you laugh, he'll make you think. He likes to run and then the thing with the... person.
Recent Seasons Update: His dad appeared in a Treehouse of Horror episode, actually voiced by Jerry Lewis!