An absolute shed load of musical genres beginning with the letter A. My favourite is top of the list - Acappella - that takes some skill that does - to come up with music from the mouth and the mouth alone.
Acappella – any singing performed without any background music/instruments.
Acid house – psychedelic style of house
Acid jazz – psychedelic style of jazz influenced heavily by funk and hip-hop production
Acid rock – a form of psychedelic rock, characterized with long instrumental solos, few (if any) lyrics and musical improvisation
Acid techno – a form of techno that developed out of acid house.
Acoustic – a music that solely or primarily uses instruments which produce sound through entirely acoustic means, as opposed to electric or electronic means.
Adult contemporary – a broad term for any music with lush and soothing qualities, and a focus on melody and harmony.
Afrobeat – a large-scaled and energetic combination of Yoruba, highlife, jazz, and funk music.
Afro-Cuban jazz – style of jazz influenced by traditional Afro-Cuban music.
Afropop – a genre of African popular music.
Aleatoric – music the compositi of which is partially left to chance
Alternative country – any style of country that deviates from the normal
Alternative dance – any combination of rock and electronic dance music
Alternative hip hop – any style of hip hop that deviates from the norm
Alternative metal – any style of heavy metal that deviates from the norm
Alternative R&B – any style of R&B that deviates from the norm
Alternative rock – any style of rock that deviates from the norm
Ambient – a form of incredibly slow electronic music that uses long repetitive sounds to generate a sense of calm and atmosphere.
Ambient house – a combination of acid house and ambient music.
Americana – a combination of all forms of roots music – folk, country, and blues
Anarcho-punk - punk rock with anarchist themes.
Anasheed – Islamic vocal music, usually sung a capella, or accompanied by a daff.
Ancient – music created in the early stages of literate cultures.
Anatolian rock - a fusion of Turkish folk and rock
Anime – music, usually J-pop, used in anime soundtracks
Anti-folk – a mocking subgenre of folk that subverts the earnest, politically-informed lyrics of folk-revivalists.
Apala – Nigerian music originally used by the Yoruba people to wake worshippers after fasting during Ramadan.
Arabic pop – pop music informed by traditional Arabic styles.
Argentine rock – rock music informed by traditional Argentine styles.
Ars antiqua – European music from the Late Middle Ages, which advanced concepts of rhythm.
Ars nova – style of French music from the Late Middle Ages, rejected fiercely by the Catholic Church.
Ars subtilior – style of French music from the Late Middle Ages.
Art pop – experimental or avant-garde pop music
Art punk – experimental or avant-garde punk music
Art rock – experimental or avant-garde rock music
Ashik – music performed by mystic or travelling Turkish, Azerbaijan, Georgian, Armenian, and Iranian bands, using vocals and the saz, performed since ancient times.
Assyrian pop music - pop, folk and dance music informed by traditional Assyrian styles.
Australian country – country music performed by Australians
Australian pub rock – style of hard rock founded in and drawing on themes native to Australian inner-city and suburban pubs and drinking establishments
Australian hip hop – hip hop performed by Australians
Avant-garde – music considered to be ahead of its time, often using new, unusual, or experimental elements, or fusing pre-existing genres.
Avant-garde jazz – experimental or avant-garde jazz music
Avant-garde metal – experimental or avant-garde heavy metal or hard rock
Avant-punk – experimental punk music
Axé – style of Salvadorian, Bahian, and Brazilian music informed by Afro-Cuban and Afro-Brazilian styles