New Orleans styles including

Funk in the Funky Meters, Galactic, Dr.John , Neville Brothers, Proffessor Longhair, George Porter Jr. style

New Orleans R&B Style such as found in the Music of Snooks Eaglin, Johnny Adams, Ernie Kdoe, Allan Tousant, Irma Thomas, Fat Domino etc

New Orleans Traditional Jazz Style-Note: This style is not the same as Dixie land there are major differences. Artists Satchmo, King Oliver, Jelly Roll Morton , Buddy Bolden, Sidney Bichet

see link: http://www.jazz.com/features-and-interviews/2009/8/26/new-orleans-100-tracks-part-one

New Orleans Brass Band music (Cross between the above styles actually)
Ribirth Brass Band, Dirty Dozen,Trobone Shorty, Kermit Ruffins- See the HBO series Treme for more examples or visit Frenchman Street in New Orleans