* Robin (Ghosts): Robin was born roughly 12000 years ago according to a tie-in book, having seen many people die and ghosts leave long before Button House was even built. While he is saddened when ghosts move on and he's left behind, because he's experienced it all before he doesn't let it bother him too much and explains that he can't experience the grief every time it happens. He's also very dismissive of Christmas until the end of the show since from his perspective it's nothing more than a passing obsession that hasn't been around very long.
* John Oldman (The Man from Earth): A 14000 year old immortal, because people always got scared of him for not growing old John fell into the habit of moving on roughly every ten years. This includes leaving behind and having no contact with any wives, children or friends that he had. When asked about this by Sandy, who has feelings for him, he explains that while he does care for his partners he's fallen in love and gotten over it too many times to really believe in it. Also it is true that as people get older their perception of time gets faster, so for John his experiences with people happen incredibly quickly from his perspective.
* Armstrong (Valiant): Aram Anni-Padda became immortal 10000 years ago when the Boon was activated, and has had countless adventures while being hunted by the Sect. It's made clear however that his drinking stems from a depression over being immortal, and how whenever he talks to people he's always aware he will outlive them and we even get his POV where learn that Armstrong sees Archer as an old man.
* Michael (The Good Place): It's only brought up in one episode, but Chidi realises that Michael struggles with fully understanding guilt and ethic because he's immortal. If he lives forever then any guilt will eventually fade so why spend so much time worrying about it? Helping Michael realise that he could potentially die helps him understand Chidi's ethics lessons.

Immortal/long lived characters who have a very different view of people and time compared to mortals.