mysql> use mysql;
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A

Database changed
mysql> update user set password=PASSWORD('password') where User='limited_user';
Query OK, 1 row affected (0.00 sec)
Rows matched: 2  Changed: 1  Warnings: 0

mysql> exit
Bye
t0nic-iMac:mysql t0nic$ mysql -ulimited_user -ppassword
ERROR 1045 (28000): Access denied for user 'limited_user'@'localhost' (using password: YES)