A teddy bear is a stuffed toy created in the shape of a bear, an Earth animal.
In 2267, after Spock's mother Amanda Grayson described a pet sehlat from his childhood as having been "like a fat teddy bear" (much to the delight of Dr. McCoy), Spock observed that these Vulcan "teddy bears" are alive and have six-inch fangs. (TOS: "Journey to Babel")
In 2368 Deanna Troi received a box of personal things of her father Ian Andrew Troi's ancestors from her mother Lwaxana Troi including a teddy bear. (TNG: "The Outcast")
A young girl living aboard the USS Enterprise-D around the time of its destruction in 2371 carried a teddy bear. Along with several other children, she was separated from her parents, requiring Lieutenant Commander Geordi La Forge to carry her to a safer part of the saucer section. The teddy bear was dropped in the scramble. (Star Trek Generations)
Julian Bashir had a teddy bear, called Kukalaka, which was his most prized childhood possession. He kept it in his possession into adulthood. (DS9: "The Quickening", "In the Cards", "Inquisition")
In 2372, The Doctor gave a white teddy bear as a gift to Denara Pel, while they were dating on the holodeck of the USS Voyager. (VOY: "Lifesigns")
In 2374, Harry Kim suggested that Tom Paris replicate a teddy bear to comfort him when nearly the entire crew went into stasis during Voyager's trip through a Mutara class nebula. (VOY: "One")