mysql: see all open connections to a given database?

As well you can use:

mysql> show status like '%onn%';
+--------------------------+-------+
| Variable_name            | Value |
+--------------------------+-------+
| Aborted_connects         | 0     |
| Connections              | 303   |
| Max_used_connections     | 127   |
| Ssl_client_connects      | 0     |
| Ssl_connect_renegotiates | 0     |
| Ssl_finished_connects    | 0     |
| Threads_connected        | 127   |
+--------------------------+-------+
7 rows in set (0.01 sec)

Feel free to use Mysql-server-status-variables or Too-many-connections-problem

The command is

SHOW PROCESSLIST

Unfortunately, it has no narrowing parameters. If you need them you can do it from the command line:

mysqladmin processlist | grep database-name