The Online Speech Bank offered by American Rhetoric and the official website of the White House are good sources for speeches. Both websites can be used for free and have extensive databases of speeches.
The Online Speech Bank by American Rhetoric has over 5,000 speeches in text, audio and video formats in its database. The website offers both speeches given by real people and fictional characters.
The official website of the White House publishes free speeches given by US Presidents, First Ladies, government officials and foreign country leaders. The website is updated very regularly, often multiple times in a day.