Reggae

Reggae is Jamaica's most famous genre, that emerged in The Sixties from Ska and Rocksteady. You probably know it because it was popularised outside Jamaica by Bob Marley, and other followers of the genre such as UB 40 and The Police.

Its main distinctive trait, asides from being played slower than Ska, is the use of the "one drop" rhythm, whereby the first beat of a bar is completely empty and the emphasis is on the third instead. To this you can add other traits, such as: harmonic simplicity, use of guitars purely as a rhythm instrument, mostly as "skank" (short, dampened, choppy sound) on the two and four beats, and occasional use of horns and other instruments.

The genre itself developed since and gave rise to several other subgenres, such as:

Dub music, probably the most famous offshoot. "Dub" basically means instrumental remixes of songs, emphasising the drum and bass (you'll find this basic track referred to as "riddim"), adding short snatches of vocals and soaking everything in lots of reverb and other studio effects. Got started as a distinct subgenre in The Seventies thanks to guys like Errol Thompson, Lee "Scratch" Perry and Herman Chin Loy. Insanely influential on electronic music (especially drum and bass and Dubstep), Punk Rock, Post Punk, Hip Hop, possibly more so than reggae itself.
Roots reggae, like normal reggae except the lyrics are largely concerned with spiritual matters and social critiques. Exponents of this include: Burning Spear, Johnny Clarke, Horace Andy (yes, the guy who works with Massive Attack), Big Youth, Culture, The Meditations, and others.
Rockers, a more aggressive way of playing reggae created by Sly and Robbie in the mid-1970s.
Lovers rock, which emerged in The Seventies out of South London and is Exactly What It Says on the Tin: reggae love songs. Examples of this include: Gregory Isaacs, Freddy McGregor, Dennis Brown, Maxi Priest and Beres Hammond.
Dancehall, probably the most divisive genre on the list. This genre uses electronic instrumentation and Sampling a lot, and involves a deejay singing and rapping or toasting over raw and fast rhythms, so it's probably closer to Hip Hop than reggae itself. Examples of this would be: Yellowman, King Jammy, Shabba Ranks, Elephant Man, Buju Banton and others. The genre's sadly infamous for aggressive, violently homophobic lyrics - for example, Buju Banton's 1993 hit "Boom Bye Bye" is about executing gay men. Probably the main source of protests and controversy due to the severe Values Dissonance between Jamaica and the rest of the Western countries over LGBT rights.