Joker and Red Hood
Whereas the Joker spent his time completely offscreen abducting Robin in Batman's gaming debut, he finally made his first actual appearance two years later in Batman: The Caped Crusader. What the game lacked in compelling combat, it made up for with standout art direction designed to emulate comic panels and bring the feeling of colorful, pre-Dark Knight Returns Batman books to life. The Joker definitely benefited from this treatment, and this remains one of his most classic looks personified in games.
Less dignified in his gaming debut was Injustice 2 DLC character Jason Todd, who's been known as the Red Hood since 2005. When The Caped Crusader was released, Jason was still pretty new at being the second Robin, and we met him in the game in one of two inglorious ways – tied to a roller coaster…or dead at the hands of the Joker as a game over scene. Somewhat ominously, the game was released within months of the infamous "Death in the Family" story arc, which saw the Joker beat Jason with a crowbar and had fans vote on his fate by calling a 900 number. By a margin of 72 votes, Jason was dead for the next 17 years.