One of the most valuable sources for Buddhist insights and teachings - from both secular as well traditional perspectives - is the huge range of dharma talks available to practitioners. Several website host talks from a variety of teachers.
Dharma Seed offers dharma talks freely (with donations/dana to the teachers encouraged) from a 'Western Buddhist Vipassana' perspective, but includes other perspectives as well.
For secular Buddhists, the dharma talks of Stephen Batchelor, Martine Batchelor, and Winton Higgins on Dharma Seed are a great place to start. Please check out the pages on this website for Stephen Batchelor and Winton Higgins for additional talks.
Other teachers whose talks are available on Dharma Seed and who sometimes discuss themes related to secular Buddhism include Stephen's Batchelor's fellow core faculty at Bodhi College: Akincano Mark Weber, John Peacock, and Christina Feldman.
Another worthwhile source of dharma talks is Audio Dharma. This site is an archive of Dharma talks given by Gil Fronsdal, Andrea Fella and various guest speakers at the Insight Meditation Center in Redwood City, CA, USA.
Tricycle's Dharma Talks
The U.S. Buddhist magazine Tricycle offers a rich resource of articles, blogs, and dharma talks, although most are not from a secular perspective.
Tricycle's Dharma Talks offers video teachings and discussions with Buddhist teachers.