The Vital Speeches Website is a great place to browse for speeches by topic. Not all are free. Use the database link above to find the fee based one.
American Rhetoric http://www.americanrhetoric.com/
Easy-to-use, searchable reference database of more than 5,000 full-text, audio, and video versions of public speeches, sermons, legal proceedings, lectures, debates, interviews, and other recorded media events. Also includes index to and database of full-text transcriptions of the 100 most significant American political speeches of the Twentieth Century.
Associated Press Videos http://video.ap.org/
Contextualizes speeches for you, plays the speech visual and audio, and gives the transcript.
American Presidency Project http://www.presidency.ucsb.edu/index.php
The American Presidency Project (APP), non-profit and non-partisan, is the leading source of presidential documents on the internet. Our archives contain 118,881 documents and are growing rapidly. The APP, hosted at the University of California, Santa Barbara, has been a collaboration between John T. Woolley (UCSB) and Gerhard Peters (Citrus College) since 1999.
Douglas: Archives of American Public Address http://douglassarchives.org/
Hosted by Northwestern University, this site provides an archive of American speeches ranging from the classic to the obscure. Users may search the archive by time period, speaker, title, or issue. Site also features links for current debates and links to resources for those studying speeches and rhetorical history.
Gifts of Speech: Women's Speeches from Around the World http://gos.sbc.edu/
A collection of speeches made by contemporary women including Maya Angelou, Betty Shabazz, Tipper Gore, Ruth Bader Ginzberg, Andrea Dworkin, Rigoberta Menchú Tum, and Margaret Thatcher, arranged alphabetically by the speaker.
History Channel.com Speeches http://www.historychannel.com/
This site has 120 Real Audio complete speeches and audio clips. There is a speech for the day and an archive of the other speeches. African-American and women speakers are included. Each speech has an explanation of its place in history.
Online Speech Bank http://www.americanrhetoric.com/speechbank.htm
Index to and database of 5000+ full text, audio and video (streaming) versions of public speeches, sermons, legal proceedings, lectures, debates, interviews, other recorded media events.
Wikipedia List of Speeches http://en.wikipedia.org/wiki/List_of_speeches
Includes those that have gained enough notability in English or in English translation to be explored in Wikipedia. Covering speeches from BC to modern times.