Super Mario Odyssey for the Nintendo Switch has no Game Overs. Whenever Mario dies, he loses a few coins and returns to the physical plane. I'm presuming Charon fishes the coins out of the plumber's pocket and paddles away laughing while Mario is left on the shores of the Styx.
From a gameplay standpoint, nixing the Super Mario series' lives system is a great idea. Lives stopped making sense as early as Super Mario Bros 3, where question blocks and end-level panels spit out free tries as readily as a listless carny. There's no longer any joy in seizing a green mushroom or hearing the 1-UP chime after collecting 100 coins.
Ah, but what's good for the player isn't necessarily good for Mario. Immortality sucks for several reasons. Immortal characters in fiction (as if immortal characters exist anywhere else) are rarely happy, even if they project a carefree façade. The people they love die again and again, their descendants become distant, and it gradually becomes impossible for them to relate to mortals. Slowly but surely, immortals' hold on sanity slips away.
And now Mario is one of them.
Sure, Mario can rack of hundreds of lives in many of his games, but a "GAME OVER" is still possible. Dying a thousand deaths to finally achieve eternal rest isn't a picnic, but at least there's a definite end to work towards.
Now that eternity sprawls before you, Mario, it might help you to hook up with some fellow immortals who understand the agony of endless life.
Ice King / Simon Petrikov (Adventure Time)
Simon Petrikov was a scholar who become immortal after donning a strange crown he bought in Scandinavia. His immortality cost him his fiancée, his sanity, and granted him the privilege of seeing the world come to ruin following a nuclear war. His mind gradually eroded until he wasn't even able to identify his surrogate daughter and fellow immortal, Marceline the Vampire Queen. I suppose Mario could sit down with Simon over some iced coffee, but not much that comes out of the old wizard's mouth makes sense. Also, his palace is overrun with murderous penguins.
Proinsias Cassidy (Preacher)
Out of all the immortals on this list, Cassidy the hard-drinking Irish vampire would probably be happiest to talk to Mario about the perils of immortality (especially if they went to a good Italian restaurant that uses plenty of garlic). Problem is, none of Cassidy's advice is bound to be much good. Cassidy thinks he has eternal life all figured out, but his philosophy to live as freely as possible has hurt more mortals than he cares to admit.
Any number of Greek gods
Show me a Greek god, and I'll show you a petulant, whiny deity who makes mortals suffer terribly whenever they throw a tantrum. Lacking a fear of sickness or death, the denizens of Olympus drift through the days with a warped perspective on what truly matters. If you're mortal, don't you dare have the audacity to perform an art better than one of the gods. Not only will you die, you'll die in a creatively horrific way. Apollo skinned a satyr alive because he was kind of good at the lyre, and Athena turned a competent weaver-woman into a spider. "Ha ha! You knew how to use a loom, and now you're a hideous bug. Dumb mortal. Imma get drunk on nectar with my pet owl."
Mumm-Ra the Ever-Living (Thundercats)
Interestingly, this dried-up villain from an '80s cartoon perfectly encapsulates the horror of eternal life. Mumm-Ra is a bent-over and fragile monster who spends most of his time sleeping because he's powerless to do much else. He can regain some strength if he calls upon evil spirits of darkness, but I imagine Mumm-Ra will gradually become so weak, he'll need the spirits' blessing to get anything done. "Ancient Spirits of Evil! Transform this decayed form into – you know what, just give me enough juice let me get up and use the can."
Princess Luna (My Little Pony)
Equestria's Princess of the Night initially had a hard time adapting to immortality, but after a long time-out on the moon, she's since learned to put her dark powers to good use. Luna's not a people-pony, but her job – watching over the dreamscape – has blessed her with an open mind and keen intuition. I think she'd get along with Mario, who's no stranger to weird worlds that are fit for dreams and fevered visions. Mario will need to control himself, though; he tends to assume all animals are mounts, and if he jumps on Luna's back without permission, I'm 99% sure she'd turn her head, lower her horn, and jab him in his right eye.