The popular usage of the word “salsa” for danceable Latin music began in 1933 when Cuban song composer Ignacio Piñerio wrote the song Échale Salsita. According to the late Alfredo Valdés Sr. whom I interviewed in 1974, he said “On July 6, 1933, I married Anita Purmuy, guitarist for the all-female band La Anacaona. I didn’t have a honeymoon because hours later I was on a boat with Nacional (Septeto) headed toward Miami…then on to the Chicago World’s Fair. On the train I rehearsed Ignacio’s new work Échale Salsita. He got the idea after tasting food which lacked the Cuban spices. It was a protest against tasteless food

Source: Latin Beat Magazine, November 1991.

Since the 1930s Merengue, which belongs to  is readily recognized as the national dance of the Dominican Republic. The most popular story relates that a great hero of the French revolution, who had been crippled in one leg was welcomed home with a victory celebration. It was known that he loved to dance but all he could do now, was step with one leg and drag the other to close. Out of respect, everyone dancing copied him and the Merengue was born. The trouble with this story is that "which revolution" is not mentioned. If it is the slave revolt then the dance originated in Haiti. If it was the revolt of Spanish emigries against the Haitians then the dance could be either Dominican or Hiatian depending on which side tells the story. 

Source: Enciclopedia Dominicana, Primera Edición

In the late 1940s, Havana, Cuba, was one of the most popular resorts for North Americans, especially those residing along the east coast. The most famous American dance bands as well as the many outstanding Latin bands native to Cuba played at the city's casinos. Some of these orchestras tried combining the American JAZZ beat with the Cuban RUMBA rhythm; The result was a new rhythm called the MAMBO.  A dance was developed to the new mambo rhythm, danced to the off beat rather than the traditional downbeat. For this reason, the dance was popular mainly with dancers thoroughly familiar with complex Afro-Cuban music. However, among the many figures of the mambo was one called the "chatch", which involved three quick changes of weight preceded by two slow steps. By the early 1950s, this figure had developed into a new dance comprised of many simple variations on the basic footwork. The dance acquired the name CHA-CHA ; its characteristic three-step change of weight carried the identifying verbal definition, "cha-cha-cha".

Source: http://www.latindanceforever.com/English/chachahstry.htm

Bachata was a musical pariah in its country of origin, the Dominican Republic. Since its emergence in the early 1960s, bachata, closely associated with poor rural migrants residing in urban shantytowns, was considered too crude, too vulgar, and too musically rustic to be allowed entrance into the mainstream musical landscape. As recently as 1988, no matter how many copies a bachata record may have sold -and some bachata hits sold far more than most records by socially acceptable merengue orquestas- no bachata record ever appeared on a published hit parade list, received airplay on FM radio stations in the country's capital Santo Domingo, or were sold in the principal record stores. Bachata musicians appeared only rarely on television, and they performed only in working-class clubs in the capital. In contrast, even second rate merengue orquestas were given lavish publicity and promotion, and they entertained at posh private clubs and nightclubs.

Source:  "Pacini Hernandez, Deboarh: "Bachata, A Social History of a Dominican Popular Music": Temple University Press, 1995.