A White Yoshi first appeared as an playable character in Yoshi's Story. One can be found in Stage 3-2: The Tall Tower or in Stage 3-3: Poochy and Nippy.
In this game, they, like the Black Yoshis, can eat things that normal Yoshis cannot, like Red Peppers and Black Shy Guys. White Yoshis can also flutter further when they're a Super Happy Yoshi, and fire eggs that explode when their happy meter is full. Also, while the Black Yoshi has the lowest pitched voice, White Yoshi has the highest pitched voice.
Yoshi Touch & Go
In Yoshi Touch & Go, after completing a 1,000 yard run when using a Black Yoshi in Marathon mode, a White Yoshi may appear randomly, which can hold an infinite number of eggs, but can only be used for one 1,000 yard run.
Yoshi's Island DS
White Yoshis appear in Yoshi's Island DS, playable in the Extra stage in each world.
Paper Mario: The Thousand-Year Door
Mario Tennis series
Mario Power Tennis
In Mario Power Tennis, Yoshi can change colors every time he performs a Rolling Egg Return, provided the player has completed the Flower Cup with any character. One of the colors that Yoshi can turn is white.
Mario & Sonic at the London 2012 Olympic Games
Mario Tennis Open
White Yoshi appears in Mario Tennis Open as an downloadable QR code character. He is a tricky type character.
Mario Kart 8
In Mario Kart 8, a White Yoshi appears as an alternate skin for Yoshi through DLC. It is available only through purchasing both the The Legend of Zelda X Mario Kart 8 and Animal Crossing: New Leaf X Mario Kart 8 DLC packs.
In Yoshi's Story, White Yoshi debuts with white skin and cyan shoes with a red saddle. This design has gone unchanged. They were also in Yoshi's Island DS, where they could be played in each world's unlockable Extra Level.