The ending cutscene of 3. The real Millennium Star allows your character to become the greatest Superstar in the universe, with the background music having that Earn Your Happy Ending feeling to it. This, combined with the credits and their music, also drives home the point that this is the last non-third-party game for the N64.
The end of the mini-game "Shy Guy Shuffle" in Mario Party 10 where the players all sit around a table eating donuts. Also counts as Crowning Moment of Funny as it is one of the few mini-games with post-game animation.
Bowser's interactions in Mario Party Island Tour's Bowser Tower when you play as Bowser jr just scream heartwarming. "Aw,who am I kidding?There's a special spot on my black heart for you,son."