The entirety of episode 53. Mario gets amnesia and actually falls for a girl. Luigi spends the whole episode worrying about where Mario has disappeared. When Mario gets his identity back, he forces himself to break it off with the girl, even though he clearly loves her. Doubles as a Tear Jerker.
In the finale, Wario and Waluigi share a warm dialogue after the Pirate Crunch bit. Waluigi also reveals that he and his girlfriend didn't break up, he just told her to stay out of the way until the danger had passed.
Pauline and DK's wedding.
The entire epilogue montage, really. Everyone who is still alive is happy and moving on with their lives.
The very last line of the series is Mario turning to the audience and thanking them for the best 5 years of his life.