Create a resource yourself. Pictures that you take or videos that you make for class are by copyright law yours to use however you like! So if it isn't possible to find a copyright free image, consider creating your own.
Use a resource that is in the public domain! Most US works created before 1930 will fall in this category, as well as images from US governmental agencies (like NASA), and works given by their authors to the public domain. Some examples of public domain can be found on the Why is Copyright Important? page.
Consider using Creative Commons Licensed materials, but be sure to understand how the licenses apply. Many will require attribution, restrict modification, disallow commercial use, or require any project where you use their resource to fall under the same creative commons licenses (i.e. you'll give up some of your own copyright privileges!)
Get permission! If you need to use a resource for class, it may be possible to license the resource or request from the owner that you be able to use it for a limited circumstance. See the "Getting Permission" page.
Creative Commons: A great place to start your search for video, audio, and images. Creative Commons has unified some of the best search engines for finding materials. Not all items will be public domain. Read all license information and use your best judgement.
Internet Archive: A non-profit library of millions of free books, movies, software, music, and more.
Flicker: The Commons: Images from archives, libraries, and museums - these images are assumed to be in the public domain, however these institutions caution that all users should do their own copyright research prior to publishing the images.
The Noun Project: A mix of creative commons licensed and for-purchase icons depicting "nouns." An account is required.
OpenClipArt: Pictures from here may be used for any purpose, including unlimited commercial productions, as royalty-free clipart, for schools, churches, commercial and non-commercial reasons.
Pixabay: A collection of images and videos that can be downloaded, modified, and re-distributed. Attribution is not required.
Free Music Archive: The Free Music Archive is an interactive library of high-quality, legal audio downloads-- some is available for reuse under Creative Commons licenses. For more information see their FAQ page.
Films on Demand (NCLIVE): for use in seated and online courses, all users (i.e. NC citizens with a North Carolina public library card) may take advantage of educational public performance rights within the database guidelines.
Project Gutenberg: This site offers over 50,000 free ebooks that may be freely used in the United States because most have entered the public domain. Particularly good for finding classic books and scientific works.
Google Books: A searchable catalog of books. Some items in the public domain can be read completely online, other items may include previews of chapters.
Open Textbook Library: A tool for finding open access textbooks with creative commons licenses in such a way that teachers and students can freely use, adapt, and distribute the material. Open textbooks can be downloaded for no cost, or printed inexpensively.