My favorite general history is Thomas Asbridge's The Crusades which is just a great general introduction to the subject. Two other excellent authors to look into are Jonathan Riley-Smith and Chris Tyerman, both have written books on the Crusades in general as well as more specific aspects of the movement.
For more specific histories, I'd recommend the following:
Peter Frankopan The First Crusade: The Call From the East. Basically a history of the First Crusade from the Byzantine perspective. It's specific focus means it's not a great overall history of the First Crusade, but it's an amazing complementary book to any more general history.
John France Western Warfare in the Age of the Crusade 1000-1300. Probably the best military history of the Crusades currently available. While it covers more than just the Crusades France is most famous as a military historian of the Crusades and his expertise on that subject is incomparable.
Anne-Marie Edde Saladin. The definitive biography of the Sultan, an excellent read all around. Definitely only pick this up if you're already familiar with the events leading up to the Third Crusade, though. Edde is not interested in re-treading that scholarship in her work and just assumes you are familiar with things like the reign of King Amalric and the failure of the Second Crusade.
Malcolm Barber The New Knighthood. Still one of the best overall works on the Knight's Templar, Barber's book is pretty dense and not very approachable but if you can stick through it there is some excellent insight in this work both into the order and the world they inhabited. His other books are also worth taking a look at.
A few that I've read and enjoyed:
Steven Runciman, A History of the Crusades, 3 vol. (1987) - A thorough narrative written in exquisite prose, Runciman remains a standard in the field, even after 30 years.
Peter Holt, The Age of the Crusades: The Near East from the Eleventh Century to 1517 (1986) - Holt gives an broader regional perspective, arguing that the main show during this period was the rise and fall of the Mamluk state—the crusades were merely coincidental. Another thorough narrative that remains well-cited.
Carole Hillenbrand, The Crusades: Islamic Perspectives (1999) - Thematic chapters, thoroughly researched, lavishly illustrated. I wouldn't recommend this as a once-over survey for the period, but it's great for researching such questions as the rise of jihad rhetoric or inter-religious daily life in the crusader states.
Christopher MacEvitt, The Crusades and the Christian World of the East (2009) - MacEvitt digs into the Christian-on-Christian relationships within the crusader states, observing that although violence occurred between Latin and Eastern Christians, they often toned down the rhetoric of religious conflict. This contributes to broader interests of historical inquiry into inter-religious conflict, providing a counterpoint to David Nirenberg's Communities of Violence (1996), which studies how religious rhetoric was used to manipulate the violence of 14c Iberia.
Ibn Munqidh, The Book of Contemplation (Penguin, 2008) - An engaging autobiography from the period, spanning Urban II's call for crusade to Saladin's capture of Jerusalem.
You might find a few further recommendations in the book list.
William of Tyre's, History of Deeds done beyond the sea, is great. A first hand account. The language is beautiful and is an easy read.
Edward Peters, The First Crusade: THe Chronicle of Fulcher of Chartres and other source material.
James B MacGregor "Negotiating Knightly Piety: the Cult of Warrior-Saints, ca 1070-1200. I particularly love this article.
Jaroslav Folda, Crusader Art is also one of my favorites.
A good trilogy that goes in-depth from the Muslim perspective of the crusades, and goes into detail about the governments of the different Muslim emirates and finally Salahuddins Ayyubid state, is Salahuddin: Establishment of the Ayyubid State, by Dr. Al-Sallabi.