The best music to accompany your videos is original music composed specifically for your video.  Perhaps you are a musician yourself, or you know one?  An alternative is to use music that is published under a creative commons license.  These licenses can allow you to use music without paying for it; usually, it just means crediting the composer.  Below is a list of websites that I have used, but there are many others.  

Here's an example of music written to accompany video.
It comes from the OPSOUND website (below) and the artist is Manola Camp  http://opsound.org/artist/manolocamp/

This site has music from just about every genre of music.  The files are well tagged so that you can quickly find the sound you are looking for.  Also, there are links to the artists' own websites.  

If you don't already know Moby, he's the guy that wrote 'Extreme Ways', which featured in 'The Bourne Supremacy'.  His site gives away versions of his music to help students making videos!  

Free classical music - great mood music for your videos.

Not a music site, but links to many free music sites.  Check them out, and if you find a good one let me know.