Kodansha International (www.kodansha-intl.com), a Japanese publisher, has probably published more books on Japan in English -- including Japanese-language textbooks -- than any other company. Available at major bookstores in Japan, they can also be ordered online at www.amazon.com.
History -- The definitive work of Japan's history through the ages is Japan: The Story of a Nation (Alfred A. Knopf, 1991), by Edwin O. Reischauer, a former U.S. ambassador to Japan. For an overview of Tokyo's history, refer to Edward G. Seidensticker's Low City, High City (Harvard University Press, 1991), which covers the period from 1867 to 1923, when the city rapidly grew from an isolated and ancient shogun's capital into a great modern city. Its sequel, Tokyo Rising (Harvard University Press, 1991), describes the metropolis since the Great Earthquake of 1923 and follows its remarkable development through the postwar years until the end of the 1980s. Describing the daily lives of samurai, farmers, craftsmen, merchants, courtiers, and outcasts, with a special section devoted to life in Edo, is Charles J. Dunn's fascinating Everyday Life in Traditional Japan (Tuttle, 2000).
Society -- Reischauer's The Japanese Today (Tuttle, 1993) offers a unique perspective on Japanese society, including the historical events that have shaped and influenced Japanese behavior and the role of the individual in Japanese society. A classic description of the Japanese and their culture is found in Ruth Benedict's brilliant The Chrysanthemum and the Sword: Patterns of Japanese Culture (New American Library, 1967), first published in the 1940s but reprinted many times since. For a more contemporary approach, read Robert C. Christopher's insightful The Japanese Mind: The Goliath Explained (Linden Press/Simon & Schuster, 1983).
For a look into life in the capital -- education, employment, home life, and more -- check your school or public library for Life in Tokyo: The Way People Live (Lucent Books, 2001), by Stuart A. Kallen. More entertaining is Tabloid Tokyo: 101 Tales of Sex, Crime, and the Bizarre from Japan's Wild Weeklies (Kodansha, 2005), by Mark Schreiber.
Culture & the Arts -- Introduction to Japanese Culture, edited by Daniel Sosnoski (Tuttle, 1996), gives a great overview and covers major festivals, the tea ceremony, flower arranging, Kabuki, sumo, Buddhas, kanji, and much more.
The Japan Travel Bureau also puts out nifty pocket-size illustrated booklets on things Japanese, including Eating in Japan, Living Japanese Style, Martial Arts & Sports in Japan, and Japanese Family & Culture. My favorite is Salaryman in Japan (JTB, 1986), which describes the private and working lives of Japan's army of white-collar workers who receive set salaries.
Fiction -- Tokyo bookstores have entire sections dedicated to English translations of Japan's best-known modern and contemporary authors, including Mishima Yukio, Soseki Natsume, Abe Kobo, Tanizaki Junichiro, and Nobel prize winners Kawabata Yasunari and Oe Kenzaburo. An overview of Japanese classical literature is provided in Anthology of Japanese Literature (Grove Press, 1955), edited by Donald Keene. Modern Japanese Stories: An Anthology (Tuttle, 1962), edited by Ivan Morris, introduces short stories by some of Japan's top modern writers, including Mori Ogai, Tanizaki Junichiro, Kawabata Yasunari, and Mishima Yukio.