Rather they be funny, cool, or the missing link. Rob from the Amazing World of Gumball originally started off as a background character, to being the antagonist of the show. He wants revenge on the main character due to blaming his lack of importance on them, as he was banished to the void (where all mistakes and uninteresting people and objects go.) Old Man McGucket in Gravity Falls was originally a joke character, to having a tragic backstory that lead to him being insane.
George Sanderson from "Monsters Inc." I think he is only in three scenes in the movie, but somehow has a complete story arc that was satisfying/fulfilling.
The RowdyRuff Boys from Powerpuff Girls started off as one-off villains but came back due to popularity
Looker in Pokémon the pokemon games. He started off as nothing more than a sequal-game joke cop, then slowly became cooler, and his most recent appearance is him taking down Ultra Beasts with the player and Anabel. Even the hint in ORAS that he could've been a victim of Ultra Space replacement made his backstory so much cooler. Lars from Steven Universe. Started off as nothing more than the "background Squidward" of the show, then begins to develop as an actual character and now he's traveling across the stars in a spaceship which I hope he gets a spin-off from. Krillin from Dragon Ball Z onwards. He gets a lot of crap for being human, but he has the most fulfilling life out of all the "Z-fighters". A job he enjoys, a family that fully supports and loves him, Friends that can save the universe. What more can you ask for? Any Star Wars background characters, because they just love to give those randos such details. That one Rogue squadron soldier? He's probably got wanted on 5 different planets and killed a wompa with his bare hands only to punch a drunken Stormtrooper in the crouch with their own blaster or something.