Every year the first Saturday of June is designated National Trails Day (NTD) in the United States. In 1987, a report to President Ronald Reagan recommended that all Americans be able to go out their front doors and within fifteen minutes, be on trails that wind through their cities or towns and bring them back without retracing steps. The recommendation became known as Trails for All Americans and led the American Hiking Society and it's members to create NTD in 1993.
Throughout the country events are planned to raise awareness of local trails and generally getting outside. Some events are like the Friends of Dinosaur Ridge event include hiking, or biking. Others like the Arvada Trails Celebration are just for fun, though Arvada's event does include a 5K walk and a 20-mile bicycle ride. Events like REI Lakewood's National Trails Day on Green Mountain involve organized trail work. Trail work events typically require registration.
To find events around Colorado check out the American Hiking Society website.