No. 4 - “Leela’s Homeworld” (Season 4, Episode 2)
This is the last episode on the list that will make you cry pure happy tears. “Futurama” is very good at using the most universal of values in ways that melt your heart. In this case, it is the love of parents for their children that is on full display. Leela, up until this point in the series, had always assumed that she was an orphaned alien, having been left on the doorstep of an orphanarium as a baby with an untranslatable note written in “alieniese.” But once she, Fry and Bender are captured by mutants (forced to live in the sewers due to their hideousness), they are subsequently released at the behest of two mysterious hooded figures. Determined to find out why, Leela tracks them down and discovers that they are her parents. They put her up for adoption as a baby when they realized that, other than only having one eye, she could pass as an alien and have a better life living on the surface. While this is very sweet in and of itself, it is the montage that follows of her parents secretly watching over her her whole life that takes this ending from a 10 to an 11.