Several times in the past, actually. The ending of "Mother Simpson", Bart failing in "Bart gets an F", Homer seemingly dying in "One Fish, Two Fish, Blowfish, Blue Fish", and the whole "You are Lisa Simpson" scene in "Lisa's Substitute" first come to mind. Then you have a whole ton of emotional but not tragic moments elsewhere such as the end of "And Maggie Makes Three", "Lisa's First Word", 'Lisa's Wedding", and so on.
Honestly, besides humor, this was probably the shows biggest strength up until season nine.