That can't be right, because the first Yoshi you encounter hadn't just hatched. He directly tells you he was off to save his friends who got sealed into eggs by Bowser, when he got sealed into one himself. Don't know what that means about the other green Yoshis in ? Blocks--the same one, sealed again and again, every time you lose sight of him? Cursed? Different Yoshis who suffered the same fate? The ones up in Star Road are clearly newborns, however.
As for this thread, Yoshi's Island is obviously going to win, and it has my vote. If I had to choose a different game, I still rather like that he was fully playable, not ridable, in Super Mario 64 DS.
Edit: Ultima Shadow, are you sure you meant Superstar Saga? They have barely any role at all in it aside from laying Neon Eggs for you!