Yoshi si Mario's pet. It says so at Nintendo.com
Here is the article:
Mario and Yoshi celebrate the Paws/LA First Annual "Animal Companion Appreciation Day"
Feb/19/02 12:00 PST
West Hollywood, Calif., February 16, 2002 -- Nintendo made a donation to PAWS/LA in celebration of the first annual "Companion Animal Appreciation Day" and the release of its new game Super Mario World®: Super Mario Advance 2 for Game Boy® Advance. Heather Tom of "The Young and the Restless" and Pamela Magette of PAWS/LA accepted the check from Mario and his ~favorite pet~, Yoshi, along with Beth Llewelyn, Director, Public Relations, Nintendo of America Inc.
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That proves that Yoshi is Mario's pet...
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"Bwa ha ha! Guess who it is, loyal Mario fans...
It is I, King Bowser... ruler of all Koopas, big and small. I have come to take over the Mushroom Kingdom (no, not the place...I mean the WEB SITE!)! Deezer, you will surrender your troops to me, or else you will never see your precious Mario again! Bwa ha ha ha ha ha ha ha ha ha!"