Since each book of the Bible was written in a particular time, place, culture, and language, I believe a study of Bible backgrounds to be absolutely essential to theological education (both in the academy and in the church). Preaching Jesus without any knowledge of the time and place He ministered would be like quoting Aleksandr Solzhenitsyn without any actually knowledge of life in the Soviet Union. Sure, you can still make your point and be a blessing to somebody, but you would be missing out on so much rich material that can facilitate our understanding of God's Word and, in some cases, be important for understanding what the inspired author is trying to say.
I currently have the privilege of teaching the youth Sunday School class at my local church. Recently we started going through Matthew's Gospel. In addition to 2 commentaries I unfailingly consult (Carson in the Expositor's series and Turner in the Baker Exegetical series), I have 3 books on Bible backgrounds that I turn to. All three of them have, to one degree or the other, given me information that has helped me bring the world of Matthew's Gospel alive (well, at least from my perspective as teacher! I can only pray that the student is getting something out of it)
[Note: for true academic research, of course, you want to consult primary sources. If you want to learn about Herod or other 1st century Jewish personalities, read Josephus, because he lived only a few years removed. If you want to learn about Jewish-Alexandrian philosophy, read Philo (who, by the way, does some stuff with mathematical interpretation of Scripture that would put Harold Camping to shame!). If you want to learn about the "nuts and bolts" of 1st century living, read the letters and documents that have been recovered from the 1st century (some of these have been published in Adolf Deissmann's monumental Light from the Ancient East). Below, however, are 3 easily-available secondary resources for the average Christian. Oh, and by the way, all 3 books have pictures, and 2 of them actually have full-color photographs, so this removes any excuse you might have for not taking a glance at them :)]
1. Everett Ferguson, Backgrounds of Early Christianity (3rd ed.; Grand Rapids, Mich.: Eerdmans, 2003; the comments below are based on my own 2nd edition copy). Ferguson is an absolute treasure trove of knowledge on everything from the Pharisees and the Sadducees to Greco-Roman education in the 1st century. Granted, not everything in the book will be as useful for the average Sunday School teacher (e.g., I don't expect to discuss 2 Baruch and its influence on Judaism with the teens in my class any time soon), but Backgrounds of Early Christianity is still hands-down one of the best resources a Christian can own for understanding the New Testament. The 1st section of this book deals with the history of Palestine from the Persian empire to the Greco-Roman world of the 1st century. The second section deals with "Society and Culture," including such topics as law, military, social status, literature, etc. The 3rd and 4th sections deal with religion and philosophy during this era. The 5th and 6th sections are perhaps the most helpful for the teacher. In the former, Ferguson discusses Judaism, including varies sects (e.g. the Pharisees), literature (the Dead Sea Scrolls, etc.), and worship (e.g. what was temple worship like in the 1st century?). Finally, in the 6th section, Ferguson deals with early Christianity, discussing such topics as pagan interaction with Christians, literary references to Christians, Christianity under imperial law, etc.
2. Victor H. Matthews, Manners & Customs in the Bible: An Illustrated Guide to Daily Life in Bible Times (3rd ed.; Peabody, Mass.: Hendrickson, 2006). This book was a Christmas present from my best friend and has already seen some good use. Although not very conservative when compared to the other two books on the list (and thus it should be read with a bit more discretion), Matthews' helpful work covers almost the entire spectrum of Biblical history from Abraham through the NT era. Although the structure of the book is laid out historically (i.e. first section is the "Ancestral Period," second section is the "Exodus-Settlement Period," etc.), Matthews' focus is not on history but rather on the day-to-day living of the average person throughout biblical history. Thus Matthews has a wealth of information on everything from marriage customs to architecture to jewelry. Oh, and the full-color photos are fantastic! (see the awesome shot of Masada on p. 189)
3. Gary M. Burge, Lynn H. Cohick, and Gene L. Green, The New Testament in Antiquity: A Survey of the New Testament Within Its Cultural Contexts (Grand Rapids, Mich.: Zondervan, 2009). The bulk of this work proceeds book-by-book through the New Testament, making it very helpful for those doing a class on a particular epistle or Gospel. In the process, the book functions as a fairly accessible NT Intro and Survey, but its true value lies in its extensive discussion of the setting and context of each book. For example, in the chapter on 1 Corinthians, Burge/Cohick/Green discuss the city of Corinth, the concept of "foolishness" in 1:23 [citing Cicero's view of crucifixion], the common practice of inviting somebody to a banquet (in light of 1 Cor 10), etc. All throughout, the authors make excellent use of primary source material (for example, when discussing banqueting in 1 Corinthians, they quote actual banquet invitations from that era). Also, The New Testament in Antiquity should get high praise not just for its full-color photographs, but rather the way in which it uses them. It is very sobering, for example, to read of Christ's crucifixion and then see a photograph of an actual 1st century man's anklebone with the nail still inside it (p. 143).
One final thought. The point of studying, whether it be the original languages or Bible backgrounds or historical theology, is not to impress one's audience (or bore them, as the case may be!) I generally do not quote D. A. Carson when teaching my class, nor do I dump on them all the information I received from Ferguson on Jewish preparation for funerals. However, just as a good house has a solid yet hidden foundation, so also those of us who get the opportunity to teach Scripture should make sure we have a solid foundation of knowledge regarding life, culture, and history in the Biblical era. The more we can make the Bible come alive, the better (especially at church!), but in order to do that, we need to understand Scripture in its own context. As Burge, et. al., write, "When Jesus told a parable, he framed it in ways that made sense to first-century farmers and fishermen. When Paul wrote a letter, he used not only his own personal cultural preferences, but he wrote to be understood, using words and ideas meaningful to a first-century audience. Today we may understand a great deal of that message, but probing its depths requires effort." (p. 17).
Naturally this is only the tip of the iceberg for great resources, so feel free to discuss more helpful books in the comments section below.