Super Mario World 2: Yoshi's Island

Super Mario World 2: Yoshi's Island, commonly referred to as just Yoshi's Island, was the spinoff of Nintendo's most successful SNES game, Super Mario World. Yoshi's Island was a drastic turn for the series, as it starred Yoshi as it's main character and used a bizarre, yet fantastic art style. Yoshi's Island is considered by many to be the greatest 2D platformer ever made.

In Yoshi's Island, Baby Mario and Baby Luigi are being delivered via stork to their parents somewhere in the Mushroom Kingdom. Along the way, the stork is ambushed by Kamek, the evil Magikoopa. However, Kamek is only able to kidnap one of the babies, Baby Luigi, while the other falls to Yoshi's Island. Conveniently, Baby Mario lands right on top of Yoshi, along with a map. It isn't long before Yoshi and his friends decide to rescue Baby Luigi and deliver the two infants to their worried parents.

Yoshi's Story for the Nintendo 64 is technically part of the same series.