亚洲Asia

欧洲Europe

非洲Africa

大洋洲Oceania (Also taught as Australia)

美洲America 

Example Sentence from Wikipedia regarding the Olympic symbol:  "In this scheme, The Americas are viewed as a single continent, and Antarctica is omitted. The current 5 continents are Africa, America, Asia, Europe and Oceania."

If you want to use them the way shenghuo798 listed them, as nouns, you must say

亚洲 The Asian continent;

欧洲 The European continent;

非洲 The African continent;

大洋洲 The Oceanian continent;

美洲 The American continent

亚洲的Asian;

欧洲的European;

非洲的African;

大洋洲的Oceanian;

美洲的American

参考资料:
http://en.wikipedia.org/wiki/Olympic_symbols#Olympic_emblem