It's important to cite quotations, even if the quotation is well-known. Please make sure that you’re using a reputable source for the quotation, such as the published transcript of a speech or something the person actually wrote (e.g., book), and then cite that source using the appropriate APA Style rules.
If you are having trouble locating a source, please contact the Librarians for assistance. There are many websites that provide quotations; however, the sites simply provide the quotations and don’t necessarily check whether or not the quotation is correct. For example, many people attribute the phrase “be the change you want to see in the world” to Mahatma Gandhi. The problem is that he never actually said that phrase (see Morton's (2011) "Falser Words Were Never Spoken" in The New York Times), so attributing the phrase to him in an essay would be factually incorrect. When you're doing academic research, the expectation is that you're checking to ensure your information is correct. Since quotations presented on quotation websites may not be correct, please avoid such websites in your scholarly research; instead, refer to a reputable source.
Reference
Morton, B. (2011, August 30). Falser words were never spoken. The New York Times. Retrieved from http://www.nytimes.com/
