The Velveteen Rabbit(1985)
Velvee, a stuffed bunny toy, is given to young Robert for Christmas. Soon, Velvee becomes loved best of all out of all of Robert's toys. But when Robert takes ill, everything he's come into contact with must be destroyed -- so it's up to the Nursery Fairy to rescue Velvee.
Based on the classic novel by Margery Williams, this is probably the best-known version of the film, and it's been released numerous times over the years on VHS and DVD.