Christians are not exempt from anxiety, from depression, or from the long effects of trauma, and the church has not always known what to say to those who suffer in these ways. Here are books I recommend on mental health. (See also my recommendations on suffering and grief.)
A word first: none of these books is a substitute for the care of a doctor or a qualified counselor, and the best of them say so themselves.
Top Recommendation

This book was extremely helpful to me as I considered people I know who have been traumatized by grief, pain, and abuse. It was helpful as I considered how I could better relate to these people and others like them, extending to them the comfort and grace of God. And it was helpful to me as both a pastor and a church member, one who longs for his church to lovingly support the ones among us who are bearing heavy burdens and carrying sore wounds.
Other Recommendations

Linne writes out of her own battle with anxiety. It is deeply theological and very practical, while deliberately staying away from areas that would be better addressed by a medical professional.

Is It Unspiritual to Be Depressed?
Written by a pastor in Ireland who himself struggles with depression, anxiety, and OCD. A well-written and helpful little book that I am certain will be a blessing to many.

For those who care for a loved one through chronic pain and long illness. It is both comforting and encouraging, and it closes with the confidence that in the end God will make all things right.

Not a book about mental illness, but about our finitude—and about receiving our limits as a gift of God rather than fighting them as a fault to be overcome.