Couple of common default user name or passwords used as follows.
admin, system, administrator, user, password, change it, manager, root, secret, secure, backdoor. Sometimes they have used the brand name as the default user name or the password.
Normally if you have purchased a new hardware you can easily find the default user name and the password with the user manual. First thin you must do is to change the default user name and the password to something else. Because someone else will be able to login to your hardware by using the default user name and password.
However, in a situation where you do not have the manuals or do not remember the user name and the password but still if you want to login to the control panel to change the configurations you will have to do a reset ( Hardware reset button will be there ) and then use the default user name and password to login and reconfigure it. When you do a hardware reset you will loose all the previous configuration and settings.
I find this default password list quite useful when it comes to login to routers and modems or any type of hardware that requires a login. Remembering the common default user name and password can save your day specially if you do not have Internet connection. Imagine a time you try to configure your router or modem to get the new Internet connection.