3. Link and Zelda - The Legend Of Zelda Series
If Mario and Peach's relationship is constant and never changing due to their consistency as characters, then the relationship between Zelda and Link is the opposite- attempting to keep things fresh by rebooting the story almost every game. While Link remains relatively similar from game to game as a ranger/adventurer with a noble heart (though his age does vary), Zelda herself gets many makeovers- from damsel in distress to mentor in disguise to pirate captain to reigning head of state to avatar of a god. Because of the myriad of Zeldas that have been created for the LoZ series, it can be argued that this romance is not quite as overtly implied as some on this list. However, there is no doubt that among most of the video game community that these two are an item and destined to be together in some form of their lives (let's face it- they have enough incarnations that one pair of them probably would hook up...). So while Mario and Peach continue with their idea of saving the princess from the evil dragon, the Legend of Zelda has attempted all sorts of ways to redecorate the furniture- yet the relationship between Link and Zelda actually remains relatively constant. I'd say that's enduring.