After riveted discussion with my wife, a lawyer, I have come upon what I believe should be the "final word" on the Copyright issues some members tend to bring up when we're talking about arrangements of music. Feel free to refer back to this thread or link to it if someone poses the question of, "Are you sure it's legal?" when you are presented with an opportunity to arrange music as a composer.
Any original work under copyright is simply known as the original work. If you arrange a work that has copyright protection, you are creating a derivative work. Without permission from the creator of the original work, creating a derivative work of the original work under U.S. copyright laws is illegal - with some exceptions. An important exception for composers to understand is the "Fair Use" exception. Here is the general gist of the exception.
The essential question of the Fair Use exception is whether or not the derivative work you've written occupies a substitute market, affecting the "market share" of the original creator. If a substitute market exists for the work you have written and you are profiting from that market, you are in violation of copyright if you do not have the permission of the holder of copyright. This is a great explanation of Fair Use of copyright works.
So, if you're a student composer, a teacher, or generally a composer who is approached to write an arrangement of music under copyright, consider the purpose of the work (is this for commercial or non-profit purposes?), the nature of the copyrighted work (is this a popular song heard on the radio being arranged for your high school band?), how much of the music you plan to use (are you writing a medley or suite?), and will your arrangement impact the market for which the original work was written? Here are some examples where copyright has been infringed, where "Fair Use" has been rejected. If I find others, I'll post them as an addendum to this.
A Junior Community College ensemble and its director re-arranged a choral work written for educational purposes, performed it once, and 47 copies of the performance were made for each member of the college choir. This was held as infringement because the choral work was written for the educational market and the composer relied on the royalties from the performance of the work as a source of his income.
A music publishing company filed a suit against the A&E network over its use of 12 seconds of the song, "Rocky Top." The Middle District of Tennessee ruled that the use by the network was not fair use, but details are sketchy since the case was settled and none of the details were released.
The point of this is to shed some light on an issue that otherwise leaves us cowering in the shadow of ignorance, fear, and paranoia. I'll try to keep updating this as I come across other cases, if only to help the rest of the community here. As the quoted portion from the U.S. Copyright Office website above, I also advise that in the event of any doubt, you should consult an attorney.