mysql_list_dbs() will return a result pointer containing the databases available from the current mysql daemon. Use the mysql_tablename() function to traverse this result pointer, or any function for result tables, such as mysql_fetch_array().
Note: The above code would just as easily work with mysql_fetch_row() or other similar functions.
For downward compatibility mysql_listdbs() can also be used. This is deprecated however.
See also mysql_db_name(), and mysql_select_db().