Another that got it right, and in a big, big way, were the anime series based on blockbuster role-playing franchise Dragon Quest.
Dragon Quest, whose first game was released in 1986 (and which continues to this day) has never really taken off in the West, but it's long been huge in Japan. So huge that it's spawned not one but two animated TV series.
The first of these was Dragon Warrior: Legend of the Hero Abel, which ran for 43 episodes between 1989 and 1991. It took its video game inspiration very seriously, structuring its episodes after levelling-up quests and usually being based around characters from the games beating up on enemies from the games.
The second series, Dragon Warrior: Dai's Great Adventure, first aired in 1991, and ran for 46 episodes until 1992. Unlike the first show, Dai's Great Adventure featured a proper, running plot, based on the popular manga spin-off of the same name.
Given the game's Japanese focus you'd expect the series to have stayed there, but die-hard Dragon Quest fans will know that the first show, Legend of the Hero Abel, actually made it to the US under the name Dragon Warrior, albeit in reduced form (only 13 episodes were dubbed).
Above you'll find a few snippets from both series, which featured better animation, better writing and in general were more faithful adaptations (in both spirit and story) than anything Nintendo's characters have ever appeared in.