他妈的

(Ta Ma De)

fuck!

this is one of the most common profanities in Chinese, its grammatically correct to begin every sentence with Ta Ma De to express your discontent.

去你媽的

(chui ni ma de)

go fuck your self

ex: chui ni ma de Bush! - Bush, go fuck your self!

The best way to cuss in Chinese is with a loud angry tone, the more obnoxious you sound the more effective it is

操你媽的

(cao ni ma de)

Go fuck your Mom! or Mother Fucker!

This one is very effective in the Chinese subway system when people are bumping into you

买肉的

(mai rou de)

Meat Seller, Butcher

This is degrading in Chinese because butchers are stereotypically ugly and very vulgar. This term is often used to degrade people as low class. 

婊子

(biao zi)

WHORE!

Add an adjective in front to make it even more offensive.

ex: 你臭婊子 (ni chou biao zi) - You stinking whore!

老不死的

(lao bu ci de)

Old head! A degrading term for old people, it literally means "you're old and you should drop dead"

狗屁

(gou pi)

Bullshit! (it litereally means "dog fart")

you can combine this with other words like

ex: 放你妈的狗屁 (fang ni ma de gou pi) - you're fucking bullshitting