The "B's" are famously clogged with the names of fine-art-music composers. I have already mentioned the great "3 B's": Britten, Bartok, and Bruckner. Oops! I mean Bach (J. Sebastian), Beethoven, and Brahms! See what I mean? Here are some more B's to get in your bonnet:
Bach (C. P. Emmanuel) was J. S. Bach's oldest son, and one of several siblings who became professional musicians. C. P. E. made the most significant impact, however. Apart from editing some of his father's works, he also composed numerous classical symphonies, concertos, and chamber pieces during his career in Hamburg. He also wrote lots of church music and vocal works, as well as a very important book on the art of playing the piano.
Barber (Samuel), best known for his "Adagio for Strings," was a 20th-century American composer. He wanted to write operas, but he only managed two: Vanessa and Antony and Cleopatra; one a Pulitzer-prize winning success, the other a total failure. It is mostly his instrumental works that are heard today, including four concertos, three "essays for orchestra," and the School for Scandal overture. He also wrote some fine songs and choral works. I recommend his choral song cycle "Reincarnations."
Bax (Arnold) was a rather silly man. Although he was a well-brought-up young man of throughly English extraction, after reading Yeats he became convinced of his true identity as an Irishman. He lived in Ireland for a while and even wrote Irish poetry under the pseudonym Dermot O'Byrne. Luckily he had returned to reality before he composed the better part of his music, which is now being revived after falling out of favor for a while. Keep an ear out for recordings of his seven symphonies, plus numerous orchestral works, tone poems, and concertos.
Beach (Amy) was the first major woman composer from America. A professional pianist, she withdrew from concertizing after her marriage to a Boston surgeon, and focused on composing instead. After her husband's death she did some of both, leaving behind an opera, a mass, a symphony, a piano concerto, and other works that are still performed today.
Bellini (Vincenzo) was one of the early-Romantic opera composers who typified the "bel canto" style, emphasizing evenness and sweetness of tone and vocal agility. Nowadays one hears scenes and arias excerpted from such operas far more often than the operas themselves. Bellini's most-often-revived operas include Norma and I puritani.
Berg (Alban) is usually grouped with Webern and Schoenberg as a leading figure in the "Second Viennese School" that produced "expressionist" and "serialist" music. Expressionism meant they depicted high levels of emotional disturbance, from tortured passions all the way to madness. Serialism meant they used mathematical principles to organize "atonal" music (music without a central key or harmonic center). Berg's opera Lulu, which I have unfortunately heard in its entirety, is a textbook example of these trends, displaying the Freudian psychological complexes of its characters so vividly that it is apt to give its audience a complex of their own. However, Berg's Violin Concerto is uncharacteristically beautiful and even consoling.
Berio (Luciano) was an experimental Italian composer of the 20th century. Much of his work was in electronic music, including pieces that he created by cutting up and re-editing recordings of the spoken word. Last year I got to hear his Sinfonia peformed by the St. Louis Symphony Orchestra and an octet of microphoned vocalists whose parts combined spoken words with singing, textless and otherwise. It was an unusual piece in that the live orchestra "spliced together" pieces by various composers, somewhat in the manner of Berio's electronic work.
Bernstein (Leonard) was a charismatic American conductor and a great popularizer of fine-art music. He was also a composer, not only for the stage (West Side Story and Candide) but also for the concert hall (beginning with the Symphonic Dances from the one and the Overture from the other). He also wrote three symphonies and the well-loved Chichester Psalms.
Biber (Heinrich Ignaz) was a Baroque-era composer, now mostly known for a series of violin sonatas based on the Holy Rosary. He also wrote some operas and church music, and is currently credited with writing a mass for a record-shattering 53 contrapuntal voices.
Billings (William) was a Boston-based composer at the time of the American revolution. Widely regarded as the father of American hymnody and choral music, his ruggedly individual (or perhaps eccentric) melodies are still sung by church and school choirs, and have been used as the basis of other compositions (such as William Schuman's New England Triptych). You can actually read one of his songs (words and music) here. Note that the melody is in the tenor line.
Bloch (Ernest) was an American composer of the early 20th century, born in Switzerland. His best-known works are a violin concerto, a piece for cello and orchestra titled Schelomo, and various compositions connected with Judaism.
Boccherini (Luigi) was a composer of the early-classical period typefying the "stile galant," a smooth, courtly style. His most celebrated works include string quintets (particularly a Minuet in E from one of them) and a cello concerto, though I have also enjoyed some of his symphonies, which share many traits with the early symphonies of Haydn.
Boito (Arrigo) was mainly a man of letters, producing writings in virtually every genre. Today he is mainly remembered as the librettist for some of Verdi's operas (including Otello and Falstaff) and for Ponchielli's La Giaconda, from which we get the famous ballet music "Dance of the Hours." (Think hippos in pink tutus. Is it coming back to you now?) However, Boito did write one famous opera: Mefistofele, based on Goethe's Faust. How famous? An excerpt from it appeared in the film Batman Begins.
Bruch (Max) was a Romantic composer now mainly remembered for his First Violin Concerto and his Scottish Fantasy for violin and orchestra. He also wrote two other violin concertos and three symphonies, which are all quite nice but not particularly original.
Busoni (Ferruccio), like Boito, wrote an opera based on Faust (Doktor Faust, completed by others after his death), but he is best-known for his insanely difficult piano music. His most celebrated works are the Contrapuntal Fantasy for piano, and the Piano Concerto that is not only the longest of its kind, but requires an enormous orchestra and even a men's chorus!
Butterworth (George) was an Englishman who wrote breathtakingly beautiful songs based on the poetry of A. E. Housman. I have sung some of them, and they are marvelous. I have also heard some of Butterworth's orchestral music played on the radio, but it's not so good. In a sad coincidence, this composer of touching songs about the tragedy of war (from Housman's A Shropshire Lad) was himself killed in action in World War I.
Buxtehude (Dietrich) was born somewhere between Denmark and Germany. He wrote mainly church music, particularly cantatas and organ works, including a number of pieces indispensible to any self-respecting Lutheran organist!
Byrd (William) was a remarkable man. A Roman Catholic who managed to avoid persecution under the Protestant reign of Queen Elizabeth I, he carried on a double life, writing Latin motets for Catholics and English anthems for the Anglican church. He left behind a well-preserved body of work, for a Renaissance composer; and though he lived to see the Baroque era, he never wrote in a Baroque style. I guess he lived by the rule: If it ain't baroque, don't fix it!