Here is a great list of 10 sites I have come across which you will be able to find most of the samples and sounds you require for your music production or anything else you might need a certain sound for. I have listed whether they are Royalty Free or if they are copyrighted in anyway as best as I can.

BBC OneMusic Sample Bank - Over one thousand samples to use in your music free (Free to use for non-commercial purposes).

DrumSamples.org - Download free drum samples for music production (Royalty FREE).

Find Sounds - Free site where you can search the Web for sound effects and musical instrument samples (Unsure about copyright of samples as finds sounds from multiple sources). This one seems to have disappeared since this post was made.

Looperman - Loads of loops, beats and samples for free for members (Membership is free though) (Royalty Free).

Philharmonia Orchestra Sound Exchange - Loads of single hits, phrases and full orchestra samples played by the Philharmonia Orchestra (Free to use for non-commercial purposes).

SampleNet - Nice set of samples, most are in Mp3 format though (Copyright Free).

SampleSwap - A completely free and lovingly maintained collection of 10,000+ quality audio samples, drum loops and vocal snippets. (Royalty Free).

Soundsnap.com - Find and share free sound effects and loops (Royalty Free). This one is no longer free since this post was made.

The Freesound Project - Collaborative database of creative-commons licensed sound for musicians and sound lovers (Royalty Free as long as you specify sample maker in credits - Creative Commons License).

Worldsamples.com - Loads of sound effects, most are free (Creative Commons License). This one seems to have disappeared since this post was made.

If you know of any others, post it in the comments of this post. Hope you enjoy searching these sites and find the sounds you want.