There are multiple possible reasons for the stairs in the Winchester Mansion that lead to nowhere. They may have originally been functional stairs that were covered up by new construction ordered by Mrs. Winchester, or they may have been designed to confuse the evil spirits she believed were haunting her.
Sarah Winchester started building the odd house on the advice of a medium who said that the ghosts of those killed by the Winchester rifle were haunting her, and they could only be appeased by building a house for them, one that could never be finished. Therefore, for 38 years, Mrs. Winchester ensured the continuous construction of the house. She was her own architect, consulting the spirits for design advice in her séance room.