Super Mario World 2 - Yoshi's Island [Continued]

    Many years would pass before trouble would befall Yoshi's Island again, allowing Yoshi and his friends to finally rest. However, in time, an old nemesis of the Yoshi clan would strike again. Over the years that passed, Baby Bowser had grown up to become the wiser and more powerful King Bowser. After several unsuccessful attempts at capturing the Mushroom Kingdom, Bowser set his sights on Dinosaur Land, the continent where Yoshi's Island is located. During the events of Super Mario World, Bowser launched his assault against Dinosaur Land. To eliminate the threat of Yoshi, Bowser magically encased the green dinosaur and his friends in Yoshi Eggs. Many of these eggs were given to Bowser's own children, the Koopalings, to be watched over. Fortunately, for some reason, Yoshi's egg escaped the confines of one of the Koopalings' castles. Instead, Yoshi's egg prison wound up in the open field of Yoshi's Island.

    Eventually, Yoshi was freed by none other than Mario and Luigi, now grown up and stronger than ever. Coincidentally, the Mario Bros., along with Princess Peach were vacationing in Dinosaur Land when King Koopa's attack occurred. As Mario and Luigi were taking a nap on the beach, Bowser's forces kidnapped the princess on behalf of their master. The two plumbers searched for Peach for hours, eventually stumbling across Yoshi's egg and freeing their old friend. Once released, Yoshi told the Mario Bros. of Dinosaur Land's plight. Together, all three agreed to rescue the other imprisoned Yoshi's and save Princess Toadstool from the forces of Bowser. Yoshi even gave the Mario Bros. a special item, a Magic Cape, to help them on their quest. 

    Yoshi proved to be an invaluable ally during this adventure, acting as a quick and powerful form of transportation for the heroic Mario Bros. The green dinosaur could use his long tongue to eat almost any type of enemy, including enemies even Mario and Luigi couldn't defeat on their own. If Yoshi was hit by an enemy, he would run away, leaving Mario or Luigi behind. However, the plumbers could simply jump back on their friend's saddle to calm the dinosaur down and continue the adventure. Unfortunately, Yoshi was unable to enter Ghost Houses, Fortresses, the castles of the Koopalings, and, ultimately, the castle of King Bowser. In these locations, the Mario Bros. had to go in alone, but Yoshi would patiently wait outside for the brothers to return.

    One morning, during the events of Super Mario World 2: Yoshi's Island, Yoshi decided to take a stroll through the jungles of Yoshi's Island. The day started out like any other day until a strange, white bundle and a map landed on his back. Inside the bundle, Yoshi discovered a small baby with a red cap called Baby Mario. Prior to this, Kamek, a powerful Magikoopa, had attempted to capture both Baby Mario and Baby Luigi as the Stork carried the babies to their parents in the Mushroom Kingdom. Kamek had divined that the two babies born that morning would bring ruin to the Koopas. As such, the powerful sorcerer knew he had to eliminate the babies before they matured. Regardless of his intent, Kamek's abduction attempt failed as he only snagged one of the babies [Luigi]. The other, Baby Mario, fell to the ground and wound up on Yoshi's back.

    However, the peace would not last long. Kamek and Bowser suddenly interrupted the peace of the Mushroom Kingdom by stealing all of the babies they could find, hoping to get all of the Star Children in Yoshi's Island DS (the Star Children were Baby Mario, Baby Luigi, Baby Peach, Baby Donkey Kong, Baby Wario, Baby Bowser, and Baby Yoshi; all but the last of these seven were captured by Bowser's forces). These seven children had special energy in their bodies that, if in his possession, would allow Bowser to take over the world. Toadies had kidnapped babies from across the Mushroom World, in hopes of finding the seven Star Children.

    Eventually, the Star Children that were kidnapped all escaped one way or another. The Stork saw the Toadies carrying the babies away, and he managed to crash into some of them, freeing Baby Mario and Baby Peach. Baby Donkey Kong's escape was not specifically mentioned, but he eventually fell from the sky and helped Yoshi (presumably a Toady had unintentionally dropped him, as an unseen baby was carried off in Baby DK's cloth). Baby Wario caused the Toadies to forcibly abandon him when he had an outrageous tantrum. Baby Bowser got into an argument with his future self, to the point where Bowser finally threw him out of the castle to Yoshi's feet. Baby Luigi was rescued last, at the end of the adventure.
    Upon reaching Bowser's Castle, Baby Bowser found no reason to further accompany Yoshi, so he immediately abandoned the group. Yoshi refused to continue without him, however, and so Baby Bowser began battling him. Yoshi quickly took the tyrannical toddler out, only for an enraged Bowser to emerge and engage in battle with Yoshi right after the young Bowser's defeat. After Yoshi managed to defeat the future Bowser, Kamek finally cut in and enlarged Bowser to an enormous size. Four Yoshi's teamed up to defeat the gigantic carnation of Bowser, and he was finally defeated for good.
    After the defeat of both versions of Bowser, Kamek and the Toadies quickly fled from the destroyed castle. The Yoshi's rescued Baby Luigi, as well as the other kidnapped babies. But soon, the Yoshi's realized that they only had six babies, when there were seven Star Children.
    However, a Yoshi is born at the end of the game, a Baby Yoshi is born, and is the final Star Child. It is likely that this Yoshi is the current Yoshi. But, because it is thought that the Green Yoshi in this game is also "the" Yoshi, the Baby Yoshi may have been born before Yoshi's Island DS, and the birth was not shown until the game's ending.
Credit to the Mario Wiki for this info on Yoshi's Island DS [Super Mario World 3]