This is from Wikipedia and an interesting take on styles.

( from WidipediA ) Music can be divided into many genres different ways. These classifications are often arbitrary and closely related styles often overlap. Many[who?] do not believe that generic classification of musical styles is possible in any logically consistent way, and also argue that doing so sets limitations and boundaries that hinder the development of music. While no one doubts that it is possible to note similarities between musical pieces, there are often exceptions and caveats associated. Labeling music with genres often do not reflect a specific culture, race, or time period. Larger genres comprise more specific sub genres.

• Bluegrass
• Blues
• Bomba
• Bossa Nova
• Cha Cha
• Cut time
• Jazz
• Jazz Waltz
• Latin

• Merengue
• Reggae
• Rumba
• Samba
• Ska
• Swing
• Tango
• Waltz

For a really big list of music styles, visit the WidipediA listing of music styles