Michelangelo's teddy bear made its first appearance in It Came From The Depths. After the turtles first met Leatherhead and dragged him unconscious to the Turtle Lair, Mikey was enamored by how peacefully Leatherhead was sleeping, and set his teddy bear down next to the alligator. But when Leatherhead woke up, he was immediately hostile, and the first thing he did was rip the teddy bear in two. Later, after Leatherhead reawoke chained to a pillar, he and Mikey quickly bonded. Mikey was shown duct-taping the teddy bear back together while asking Leatherhead his name.
The teddy bear appears again in Pizza Face when Mikey was shown sleeping with it. It is the same bear, having the same duct tape Mikey used to repair it after Leatherhead ripped it apart.
The Croaking reveals that the same teddy bear was a meaningful belonging Mikey had taken with him to the O'Neil Farm. He wrapped it along with a box of Hellio's pizza when he tried to run away from home.
In Lone Rat and Cubs, it is revealed that Mikey has had that teddy bear since he was a baby.