The Other Mario Movie
Not to toot my own magic flute, but I know a lot about videogames. But I had no idea a Mario Bros. anime existed.
Super Mario Bros.: Peach-Hime Kyushutsu Dai Sakusen! was released in 1986 and never made it out of its Japanese homeland. Directed by ex-Sanrio employee, Masami Hata, this was the very first film based on a videogame. It was first released in theaters (which is strange considering its 60 minute runtime) and then on VHS, never to receive a DVD version.
Need this in your collection? Unfortunately, all the coins in the Mushroom Kingdom couldn’t get you copy. Apparently the tape is even hard to find in Japan, let alone the West. Its Wikipedia page even claims it to be one of the rarest films of all time.
Someone must have gotten a hold of one though, since you can view its fansub on YouTube.