One thing that is true about all piano teachers is that they like music--so you can't go wrong with a CD, right? Not so fast--do your homework, and find out what kind of music he or she listens to outside of lessons. Is she a jazz buff? Does he collect vinyls? Keep an eye out for hints throughout the year so that when the time comes, you have an idea what to get. And as always, include a gift receipt.
Some people have a very close relationship with their piano teacher; if this is the case, then consider framing a picture of the student and teacher, perhaps playing at or after a recital. This idea is easy and personal, and it reminds the teacher of his or her accomplishments. Be creative--this gift can be anything from homemade to a custom framed-and-matted project.
If your child is the student, think of ways you can incorporate his or her artwork into a present. Has she finger-painted a picture frame? Has he crafted a macaroni Christmas ornament or painted a candle in art class? Keep it simple. If you are an adult student, too, don't rule this out--are you a woodworker, artist, chef? Do what you do best, and share some of it with your instructor--that's what she does for you.
Don't think that piano teachers get this all the time! Chances are, he would love to update his musical score collection. Consider a series by his favorite composer or editor; there are plenty of deals available online as well as in local music stores. Again, make sure she doesn't have it already, and that it's one you think she wants. Remember, sheet music includes everything from the latest pop song to Bach inventions to musical theatre--don't get stuck in just the marching band section.
For a very special person, compose (or have your child compose) an original piece. Skip the cheesiness of naming it after her. Instead, put what he's taught you to practice. Are you working on mastering 3/4 time, or studying advanced music theory? Wherever you are in your study of piano, your teacher wants to know you're listening, and wants to share his love of music with you. Sometimes the best present is returning the favor.
Also, think carefully about how you will present it. Do you have the means to record it on CD or tape? Can you surprise her with it at a recital? Or, will you play it for him in private, perhaps before or after a lesson? Choose a method you think will please your teacher the most.