Use the show databases command as demonstrated below:

[root@probe root]# mysql -u root -p
Enter password:PASSWORD
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 21 to server version: 3.23.58

Type 'help;' or '\h' for help. Type '\c' to clear the buffer.

mysql> show databases;
+----------+
| Database |
+----------+
| mysql    |
| test     |
+----------+
2 rows in set (0.00 sec)

mysql> quit
Bye
[root@probe root]#