Ska: tsunami bomb, bim skala bim, the suicide machines, planet smashers, mighty mighty bosstones, the insyderz, B.O.B. (*if you like christian music at all), mephiskaphales, skatalites, OC supertones, Catch 22 (part of the band from streetlight manifesto),operation ivy, the specials, Big D and the kids table, Buck o Nine, fishbone, mad caddies, spunge, skankin pickle, the toasters, don drummond, Rancid (some albums more than others)
Reggae: The Expendables, Rebelution, Bob marley and the wailers, UB40, 311, Anyone that ends with the last name marley (there's a lot of them), The Ethiopians
Jazz: Herbie Hancock, the yellowjackets, after hours, the seatbelts(cowboy bebop music), Stevie Ray Vaughn (tin-pan alley), Santana (obviously), Benny Goodman, Artie Shaw, Thelonius Monk, Louis Armstrong, Ella Fitzgerald, Billie Holiday, Red Nichols
On a related note almost all of the bands for ska and reggae cross over into each other one time or another, ska is essentially punk and reggae, and reggae could even be looked at as just slow ska with weed lol.
Hope this helps!!!