Every serious musician has a large collection of sheet music. The problem is that sheet music books are not well suited for traditional bookcases. For one thing, they usually don't have hard covers and the format is almost universally oversized, compared to "regular" books. As a result, special furniture styles had to be developed. Such furniture pieces can be special ordered or bought ready. Here are a few things that you need to keep in mind when looking for ways to organize your sheet music.
The absolute best way to store sheet music is to do so horizontally. This preserves the books very well, they will be in best shape when used for performances. There are two distinct styles of furniture that can be used for these purposes: cabinets and open shelves. Cabinets protect sheet music from dust and light. They provide an easy way to categorize sheet music.
Open shelves, on the other hand, can be very ornate. Having too many shelves would be unsightly, so if you have many different categories of music (chamber, orchestra, piano etc) organizing your sheet music is not easily achieved with this style of furniture. However, in a music room such shelves can create great romantic atmosphere. And of course, you can combine the two styles, the open shelves and utilitarian cabinets.
For a more modern look and portability plastic crates are often a valid solution. Finally, wicker baskets can be a nice touch as long as the design of your music room is compatible with this somewhat rustic look.