Love Hina: Christmas Special. After an entire series of Keitaro's ass getting kicked, Naru's reveal that she'll go to Tokyo U with him gets 'em flowing every time.
It comes full circle in the Spring Special wherein Naru's sister congratulates Naru for making it into Tokyo U. Even she can't hold back the tears.
And in the TV series, the story of Moe the automaton and her awakening, restoration, and descent back to motionless silence provides a surprisingly emotional diversion in a normally lighthearted story. The scene that plays out to Yui Horie's "Yakusoku" song in episode 24 qualifies too.