How do I remove a MySQL database?

From the MySQL prompt:

mysql> drop database <db_name>;

If your database cannot be dropped, even though you have no typos in the statement and do not miss the ; at the end, enclose the database name in between backticks:

mysql> drop database `my-database`;

Backticks are for databases or columns, apostrophes are for data within these.

For more information, see this answer to Stack Overflow question When to use single quotes, double quotes, and backticks?.