The Squishy Bunny is one of Mr. Big's treasured items. It's almost always in his pocket, or in his hand. As he is constantly squishing it, the Squishy Bunny's squeak has a familiar tone, a bath toy squeak, to be precise.
In the episode "Leslie Makes It Big", Leslie built a mind-control device in the form of a giant Squishy Bunny. She was probably inspired by Mr. Big to make a Bunny.
Mr. Big once bought a special Bunny through the mail, claiming it was the squishiest Bunny ever to be squished by mankind. But it was used as a diversion near the end of the episode, so it is unclear if he has it currently.