Hollywood style is very popular on the west coast of the US, though is danced all over the USA and other countries as well.
The style was the style seen in the 1940's movies, with Dean Collins, Hal Takier, Jean Veloz and others. It is seen as a fun upbeat dance with tons of oppurtunities to expand the style and make your own moves. The Swing Out (the basic step of lindy) is danced sitting a bit lower to the ground and you do not stand up as much as Savoy. A pike is the classic look of Hollywood it is done by bending one leg slightly like you are beginning to sit down and sticking the other leg out straight with your back straight and slightly tilted forward.
One variation is LA style Lindy.