Mario and Princess Peach are apparently just friends, according to Nintendo.
A recent update to Nintendo's 'Today' app stated, "Princess Peach and Mario are good friends and help each other out whenever they can," asserting that the plumber was not a suitable match for the princess.
Mario famously saves the princess from the evil Bowser in most Mario games, and in some, it's implied that the duo are a couple. In Super Mario Odyssey, Mario attempts to propose to the princess as she gives him kisses, and on Valentine's Day 2014, Nintendo's X account posted a picture of the two of them.
For all of Mario's efforts in saving her, it seems he's destined to be in the friend zone.
Interestingly, Peach wasn't Mario's first love interest in the games. In Mario's first ever appearance in the 1981 Donkey Kong, Mario is tasked with saving Pauline from the giant ape, an entirely different woman whom the game introduced as Mario's girlfriend.