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):

1. Copying to avoid purchase
2. Copying music for any kind of performance (but note the emergency exception below)
3. Copying without including a copyright notice
4. Copying to create anthologies or compilations
5. Reproducing materials designed to be consumable (such as workbooks, standardized tests, and answer sheets)
6. Charging students beyond the actual cost involved in making copies as permitted above

What you can do without having secured prior permission:

• Emergency copying to replace purchased copies which for any reason are not available for an imminent performance provided purchased replacement copies shall be substituted in due course.
• For academic purposes other than performance, multiple copies of excerpts of works may be made, provided that the excerpts do not comprise a part of the whole which would constitute a performable unit such as a section, movement, or aria but in no case more than 10% of the whole work. The number of copies shall not exceed one copy per pupil.
• Printed copies which have been purchased may be edited OR simplified provided that the fundamental character of the work is not distorted or the lyrics, if any, altered or lyrics added if none exist.
• A single copy of recordings of performance by students may be made for evaluation or rehearsal purposes and may be retained by the educational institution or individual teacher.
• A single copy of a sound recording (such as a tape, disc or cassette) of copyrighted music may be made from sound recordings owned by an educational institution or an individual teacher for the purpose of constructing aural exercises or examinations and may be retained by the educational institution or individual teacher. (This pertains only to the copyright of the music itself and not to any copyright which may exist in the sound recording.)

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)