The North Shore is world renowned for its mountain biking. Mount Fromme and Cypress Mountain are the two more well-known areas for downhill biking. An excellent resource for finding trailer is Trail Peak. Check out the excellent North Shore Mountain Biking Association for more details.
Chilliwack (100 or so kms east of Vancouver) also has well known biking trails. The Vedder Mountain Trails Association manages the trails, and provides maps and descriptions on their website.