Answer:
There are two basic philosophies about this: either group all biographies together, or classify them according to the topics to which their subjects are most relevant.
For example, Library of Congress classification reserves ML410 for biographies of individual composers, and Dewey classification reserves 780.92 for the same.
The advantage of this method is that a biography of Beethoven will be in the same area as a book about his symphonies, or the scores of his symphonies themselves. Also, if there is a separate music library, it is easy to tell what range of classification will be in that location (for LC, classes M, ML, MT; for Dewey, the 780s); all the music books will be under those classifications.
On the other hand, many public libraries (especially smaller libraries where the entire collection is accessible on one floor of a facility), and school libraries, may find it better to group all biographies together, alphabetized by the subject's last name. Dewey classification reserves the numbers 921-928 as an optional location for biographies grouped this way, and many Dewey libraries simply classify all biographies under "B" or some other locally-determined moniker, then file by the subject's last name.
The advantage of this method is ease of browsing and self-serve access for users whose reading interests are not as subject-specific, and especially for K-12 students who frequently have to select a biography for a book report.