Music copyright can be a very complex area to navigate. A single musical work can have two separate copyrights: the composition (music and lyrics) and the recorded performance of the work. And the original composer or lyricist or performer doesn't necessarily own the copyright after it has been published. For more info on the various licenses required to record, etc. see the EMG web site
Consider the four factors of fair use before making a copy. The following, however, are expressly prohibited (from the Music Publishers Association website):
What you can do without having secured prior permission:
See also the Royalty-free Resources tab in this guide
From the UW Office of General Counsel:
The UW System has negotiated System-wide licenses with ASCAP (American Society of Composers, Authors and Publishers), BMI (Broadcast Music Inc.), and SESAC (Society of European Stage Authors and Composers), which are organizations that represent their member composers and music publishers in the licensing of non-dramatic music performing rights in musical compositions. The ASCAP, BMI and SESAC licenses cover the music performing rights for live or recorded performances of copyrighted works in concerts (unless promoted by outside promoters), sporting events, and other events, such as orientation and graduation events, on the university's premises. The licenses also cover transmission of such performances over campus computer network or cable television sytems. The licenses do not cover music performed live in a play where the music is an intrinsic part of the dramatic action. Such performances involve so-called "grand" performing rights and are not within the scope of the ASCAP, BMI or SESAC licenses.
The ASCAP, BMI and SESAC licenses also do not cover synchronizing sound recordings with video images in any medium such as on a DVD or on a website. Synchronizing copyrighted music to video images requires a separate synchronization license which can be costly and difficult to obtain. In these situations it may be more efficient and cost-effective to use “cleared music” which is available from a variety of providers for free or a small fee...
(see tab in this guide, Royalty-Free Resources)