For me, The Simpsons was a great show because of the cast of hilarious peripheral characters. I enjoyed their brief appearances more than their full episodes. And of all the hundreds (thousands?) of secondary characters, my three favorites have to be Ralph Wiggum (no surprise there), Kearny and Millhouse's Dad, Kirk Van Houten.
Ralph Wiggum: Ralph is the king of the quick, one-sentence cameo and his lines are almost always quote worthy. "Go Banana!", "Mrs. Krabappel and Principal Skinner were in the closet making babies and I saw one of the babies and then the baby looked at me", and "Hi Super Nintendo Chalmers." I think I was so attached to Ralph because I knew a kid growing up who, though not as dim as Ralph, was fairly close in intellect. He once asked sincerely when Hedgehog Day was. He then told me that he "ated the purple berries. They tasted like burning."
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Kearney: Kearney is a good example of something the writers of The Simpsons have done exceedingly well over the years: character development. When Kearney first appeared he wasn't much of a character, he was just one of Jimbo's lackeys. But as the series has progressed, little tidbits about Kearney's life have been slowly revealed making him much funnier. He is divorced. He's about ten years older than everyone else. He has a kid. Just as Ralph reminded me of my stupid friend, Kearney's evolving status as the really, really old kid in class is pretty universal. I had a friend who had his learner's permit by 8th grade and was shaving in 5th grade, much like our beloved bully, Kearney (although Kearney had his license by 5th grade). Unlike Kearney, his child did not sleep in a drawer.
Millhouse's Dad: Like Kearney, Millhouse's Dad has been evolving as a character from his first appearance. When he and Luann split, he starts to become the perennial loser we know him as today (This episode is also the source of a great Kearney quote: "Ah, you'll do fine. My divorce was tough on my kid, but he got over it."). The series of jobs he's held are so astoundingly terrible I wonder how the writers think of them. Assistant to the guy who puts fliers under windshield wipers? Amazing. He's the perfect loser: incapable of catching a break, progressively more pathetic and, best of all, bald. His pathetic whimpers and pleas are the stuff laughing fits are made of. That being said I would pay great money for Kirk's debut CD, "Can I borrow a feeling."