Belly dance styles also deserve their own alphabetical list:
Baladi, Ballady, Balady
Egyptian - a very large umbrella of styles... searching for a difinitive description (suggest on, or call back later?).
Folkloric - An equally huge amount of belly dance stems from a variety of Folkloric dance styles. The term is frequently used to mean a movement is performed in an "easily accessible" manner. So, a person "giving it a go" would not need special flexibility training to perform the majority of moves. Folkloric styles were (possibly) the starting point for more 'processed' styles, and the influence is now a two-way flow.
Guedra, a style associated with a specific drum rhythm & a specific culture. Described by Morocco on the website at: http://www.orientaldancer.net/articles/guedra.shtml
Khaleeji, Khaleegy, Kalijii
Raqs sharqi - has a website which is a good place to start learning about the history of this style: http://www.raqssharqisociety.org/index.htm
Saiidi - the description of Saiidi style posted on this website: http://www.mayada.ca/saiidi.htm appears to be clear and concise.
Tribal in all its splendid variety - American Tribal Style (ATS) is described by Carolena Nericcio on the FCBD website: http://www.fcbd.com/about/ Gypsy Caravan, Kiwi Iwi and more.
Turkish - there appears to be many discussions about the stylistic differences between, for example, Egyptian & Turkish dance styles. A description for Turkish appear on the Wikipedia website at: http://en.wikipedia.org/wiki/Belly_dance#Turkish_forms
Links and information contributed by Abijii, Anoushka, LeQuaia, TH, LF, LJ.