Apart from Grandpa's intermittent paranoid obsession with "Dea-ea-eathhhhhh!!!!", the first of life's two inevitabilities has affected the series in many ways, both in real life and within the context of the show.
-Although no screen time was ever devoted to it, recurring character Dr. Marvin Monroe, Ph.D., met his demise in season 7. He reappeared several years later in 'Diatribe of a Mad Housewife' claiming that he was "very sick". The character was retired as it placed a strain on Harry Shearer's voice.
-Blues/jazz saxophonist "Bleeding Gums" Murphy died in season 6, in an episode entitled "'Round Springfield" (a play on the 1986 film "'Round Midnight" about the gradual demise of a once-great jazz musician). His passing was really the primary plotline of the episode, with his appearance in a bed at Springfield General sparked by Bart's winding up at the same hospital after swallowing a jagged metal Krusty-O.
-Frank Grimes, a one-time character to whom Homer was his greatest nemesis, prevented Homer from falling to fatal mistakes several times during the episode and then, ironically, died while performing a mocking impression of Homer and grabbing two electrical nodes, completing the circuit and electrocuting himself.
-Repressed teetotaller Maude Flanders, wife of Ned, mother of Rod and Todd, met probably the most high-profile death in the show's history, with an entire episode devoted to her passing (she was knocked out of the top row of a racetrack bleachers onto the concrete pavement below by a ballistic t-shirt) and Ned's struggle to cope with the loss. It is generally considered to be one of the most poignant of the show's episodes, as well as one frequently cited in real-life church sermons by clergymen attempting to relate to parishioners' pop culture sensibilities.
-Phil Hartman voiced legendary recurring characters Troy McClure ("You may remember me from such {plural media format} as....") and Lionel Hutz, Attorney-at-Law, the worst attorney (and real estate salesman) in Springfield. In 1997, his mentally ill wife Brynn shot and killed him and then herself at their home in Encino, Calif. As a result, the characters simply ceased to exist among the Springfield populace, although no mention of either of their deaths was ever made.
-Veteran script supervisor-turned-voiceover actress Doris Grau voiced several different characters over the show's first seven seasons, most notably recurring character Lunchlady Doris. She died of an illness in late1995 at the age of 71.
-The character of Hans Moleman, the short, bald, eyeglass-wearing senior citizen, is never actually seen dying on-screen, but he has the tendency to end up in situations where survival seems next to impossible (e.g. crushed under a pile of burning cars). However, he always returns after some episodes without explanation (but it should be noted that the series is not known for its strict sense of continuity).
-Homer's Mom, who had left Homer and Grampa for a group of Radicals back in the 60's came back into Homer's life a few times, but the last time she returned her and Homer had a falling out and she passed away over night while sitting in front of the fireplace. The episode was dedicated to Dan Castellaneta's mom
-Some of the most violent deaths in the series can be ascribed to Itchy and Scratchy, but they are supposed to be animated characters (The Simpsons being an animated series itself notwithstanding).
-The character of Dr Nick Riviera was impaled by a large shard of glass in The Simpson Movie, and has been recently seen alive in the season 20 episode "Lost Verizon."
-Of course, no discussion of death's impact on "The Simpsons" would be complete without mentioning the various ways in which the show's characters, and the world at large, bought it in the various "Treehouse of Horrors" Halloween episodes. However the segments are non-canonical to the core Simpsons chronology.