Freesound.org is a great website utilized by professionals in the music and movie industries. If it's good enough for them, then it's good enough for you.
99sounds.org is a website that offers free content created by its own users. Every month they have a new pack available for download, so you can keep working on your game, and let 99sounds.org worry about the music.
If you need a sound fast, then noiseforfun.com is the one for you. You don't need to register and the sounds are organized by genre, making it even easier for game creators to find what they need.
Incompetech.com beats out its competitors by allowing you to sample even just parts of a song that you like and download those individually. If you are a picky listener, then this might be the website for you.
This is a website that started out dealing with free game art, but you can also download sounds as well. Users share their sounds and choose what license to share them under, and you can interact directly with the users who create the sounds using their forum.
RaisedBeaches.com stands out because of it's Octave collection. This is a selection of UI sound which come in .aif form. It consists of forty-eight beeps and clicks that you can download directly.
Musopen.org is there for anyone with a more retro taste. While it still has modern sounds, this site also has a large collection of classical music to choose from and allows you to preview tracks before download.
PlayonLoop.com is a sister to Noiseforfun.com and offers background loops. Most of their content is not free, however if you choose a shortened loop, you don’t have to pay but will be asked to attribute the site.
Bensound.com has a fantastic array of music and sounds available for free. If you are looking for a fast find, this could be it.
SoundJay.com works as a standard site, up until you find the miscellaneous section which houses some very obscure but needful effects.