October 13th is not a special day in terms of a widely recognized holiday or event. However, there are several observances and events that occur on this day. Some of these include:

• National No Bra Day: This day is observed to raise awareness about breast cancer and encourage women to forgo wearing a bra for the day.
• Navy Birthday: This day celebrates the establishment of the United States Navy in 1775.
• National Yorkshire Pudding Day: This day celebrates the iconic British dish, Yorkshire pudding.
• Disaster Day: This day is observed to raise awareness about the importance of disaster preparedness and response.
• Ancestors Day: This day is observed in some cultures to honor and remember ancestors and their contributions to the family and community.
• International Civility For the Girl Child Day: This day is observed to promote civility and respect towards girls and women.
• English Language Day: This day celebrates the English language and its global significance.
• Prince Louis Rwagasore Day: This day honors the life and legacy of Prince Louis Rwagasore of Burundi.

In addition, there are several historical events and famous birthdays that occurred on October 13th, such as the Battle of Hastings in 1066 and the laying of the cornerstone for the White House in 1792.