John Macarthur's ministry Grace to You and R.C Sproul's ministry Ligonier both offer a rotating list of free books. Biblesforamerica.org is an another resource that sends out free Christian books on various topics.
Biblesforamerica.org has a short order form that can be completed in under a minute, and visitors receive the books they request in around four weeks. Often, the Grace to You and Ligonier ministries announce in their radio broadcasts that by contacting them as a first-time listener or as someone who has never received a free book, you can request a copy of a certain title. Both ministries have websites by which you can contact them for a free book if you do not listen to the radio broadcasts.
As of November 2015, the title offered by Grace to You is "Grace For You," a booklet about Christian redemption pulled from a larger Macarthur title, "A Tale of Two Sons." The current book offered by Ligonier is an introductory text for those who are curious about historical evangelicalism and God's grace entitled, "What is Reformed Theology?"
Another ministry that offers free resources is Desiring God, which was founded by John Piper. There are 24 books offered for free on Desiringgod.org. However, these books only come in EPUB, MOBI and PDF formats, and the ministry does not mail them for free.