They're not necessarily songs that you may have heard before, but work well for background music.
Some of the following are free under certain conditions, some are Creative Commons, again with varying conditions. You will need to check what conditions apply to the tunes of your choice.
YouTube Creator Studio includes music, sound effects for free. Some commercial music is available depending on its use and publication.
Freesound is a collaborative database of CC licensed sounds. MUSIC AND SFX
Musopen is a non-profit focused on increasing access to music by creating free resources and educational materials.
Free Music Archive is an interactive library of high-quality, legal audio downloads directed by WFMU, the most renowned free-form radio station in America.
Incomptech is Kevin MacLeod's public portfolio.
Jamendo is a source of free and paid legal music downloads, although not all free, many tracks are available under Creative Commons license.
Rumblefish A website where you can search for and purchase licenses for audio files for use in published videos.
CCMixter Free, copyright-free music.
Creative Commons If you want to add music to your learning objects, this site allows you to find and legally acquire licensed music. It also includes links to many free music web sites that offer music published under Creative Commons’ flexible copyright licenses.
Derek R. Audette copyright music, sound effects
Internet Audio Archive Contains over two hundred thousand free digital recordings, many which are free.
Magnatune Includes music that can be legally used in non-commercial podcasts and projects.
AudioMicro.com has about 2,000 free sound effects that I found to be of good quality.
freeSFX has several thousand free sound effects that are also of very good quality. They also have hundreds of categories, so it’s pretty easy to find the exact type of sound you are looking for.
99Sounds is a cool site because it has a bunch of collections of high quality sounds created by various sound designers. The collections are quite large and the audio quality is superb.
FreeSound FreeSound is a database of browsable, downloadable sounds under a Creative Commons License.
Partners in Rhyme Royalty-free sound effects.
Macaulay Library from the Cornell Lab of Orinthology The world's largest archive of wildlife sounds. http://macaulaylibrary.org/terms-of-use
Sound Bible--Royalty Free Sounds SoundBible.com offers free sound clips for download in either wav or mp3 format. The clips on the linked page are royalty-free (please note that clips elsewhere on the site may not be royalty-free).
BBC Sound Effects 16,000 sound effects in downloadable WAV format for personal, educational use
National Jukebox from Library of Congress
The Library of Congress presents the National Jukebox, which makes historical sound recordings available to the public free of charge.
Links to over 4800 free to download classical performances on the internet, sorted by composer and work.
Audio and MP3 library containing over 2,000,000 free digital recordings ranging from alternative news programming, to Grateful Dead concerts, to Old Time Radio shows, to book and poetry readings, to original music uploaded by users. Many of these files are available for free download.