The school I go is called the Chinese Shao-lin Center. As for styles, we learn basically al the Chinese styles. An abbreviated list is:
External and Animal Styles:
Northern Fist
Southern Fist
Whirling Palm
Tiger (of the Flying, Golden, White, and Black variety)
Crane (various styles; I only know a little White)
Snake (Golden Snake is the highest-level style of our school - only our grandmaster knows it)
Leopard (various styles thereof)
Dragon (various)
Eagle Claw
Praying Mantis (various styles)
Monkey (various)
Shao-lin bird
Eight Drunken Immortals
Hua Mountain Fist
...and a bunch of others that I've forgotten
Internal Styles:
Tai Chi (Yang, Chen, and Wu styles)
Pa Kua (Classical, all 8 animals, and others likely)
Hsing-I (5 elements, 12 animals, and probably others)
Meteor fist (I don't really know much about this one)
Weapons:
Staff
Single/Double nunchaku
Short stick
Chinese broadsword
Straight sword
Spear
Kwan Tao
Three-sectional staff
Sai
Tiger-hook swords
TaMo canes
Butterfly swords
The various, crazy-looking Pa Kua weapons
...A bunch of other random ones that are less common.
So, yeah...we learn a lot of different styles. The one that I'm working on perfecting and getting to a useful level of competence right now is my drunken style