Following is a list of some books about Islam that I have read and found informative and/or enjoyable. All books are available from Amazon.com unless otherwise noted.
The Heart of Islam, by Seyyed Hossein Nasr. A great introduction to Islam for both Muslims and non-Muslims. Learn about the spiritual principles of Islam and how they are given form in the religion. Discover what Islam says about peace, justice, and love.
An Introduction to Islamic Cosmological Doctrines, by Seyyed Hossein Nasr. This book requires some familiarity with Greek philosophy, and it contains sections in Arabic, German, and French that are not translated, so it is not for the beginning reader. However, it rewards careful study and shows the sophistication of Muslim thought in the 900s and 1000s CE.
The Lawful and the Prohibited in Islam, by Yusuf al-Qaradawi. A simple, clear guide to living life according to Islamic law. Probably the best reference on this subject that is available in English. Very highly recommended.
Muhammad: His Life Based on the Earliest Sources, by Martin Lings (Abu Bakr Siraj ad-Din). This book is primarily based on Sirat Rasul Allah by ibn Ishaq (recension by ibn Hisham) with supplemental information taken from the "six sahihs" hadith collections, the biographies of ibn Sa'd, and the history of Tabari. It is written in a wonderfully clear and engaging style.
Qur'an and Woman, by Amina Wadud. A fascinating and provocative analysis of the Arabic text of the Quran showing the equality and complementarity of men and women according to Allah's revealed Scripture.
Studies in Early Hadith Literature, by M.M. Azami. Shaykh Azami sets out to prove that the hadiths were being transmitted and taught in writing as early as 50 AH. As much information as you could ever want to prove the authenticity of the hadiths.
The Tao of Islam: A Sourcebook on Gender Relationships in Islamic Thought, by Sachiko Murata. Like Nasr's book on cosmological doctrines, this is not for the beginning reader. As well, it will appeal best to those with an interest in tasawwuf (Sufism). Most interesting is the comparison between Islam and the Far Eastern religious worldview, not a perspective that is often seen. The author is a Japanese Muslim.
To be a European Muslim, by Tariq Ramadan. This book should not be read only by Muslims in Europe. Rather, it is for every Muslim living in the West. How can we stay true to Islam while living in non-Muslim countries? This book examines the problems, then offers solutions that are entirely Islamic. A must-read for Muslims in the West.
Traditional Islam in the Modern World, by Seyyed Hossein Nasr. All about the collision between traditional Islamic ways and the modern West. Learn how rich Islamic culture is and how to avoid pseudo-Islamic ideas that are really just Western teachings in new trappings.
Veil: Modesty, Privacy, and Resistance, by Fadwa El Guindi. A thorough look at hijab in Islam and its many aspects. Decisively refutes misguided Orientalist and feminist ideas about hijab.
The Vision of Islam, by Sachiko Murata and William C. Chittick. If you want to know what the Islamic tradition teaches about religion itself and its dimensions, read this book. Very highly recommended. This book was a significant factor in my decision to convert to Islam.