In case you have opted to receive notification when you login through new computer or mobile device, Facebook asks you to name the device next time you login and adds it to your Facebook Account. As soon as you do that, you will receive a notification on email.
Below is snapshot where I was asked name the computer from where I logged in for the first time.
The Email received for the new device :
Hi Ashish Mohta,
A new device named “Aryan” was added to your Facebook account (Today at 11:10am).
If this device was added without your permission, please remove it from your account immediately, then change your password.
If this was an authorized login, please ignore this email.
To remove this device and change your password:
1. Log into www.facebook.com.
2. Click the Account tab at the top of the screen and select “Account Settings” from the drop-down menu.
3. Scroll down to the Account Security section and click the “change” link.
4. Find the name of the unauthorized device and click the “remove” link next to it.
5. Scroll up to the Password section of the Account Settings page.
6. Click the “change” link on the right and follow the instructions.
To learn how login notifications can help you to protect your account information, visit the Help Center: http://www.facebook.com/help/?topic=loginnotifications.
Please note: Facebook will never request your login information through email.
The Facebook Team
Where you can see the list of device added to your Facebook Account :
Go to Account Seetings > Account Security. Here you will see the date on which the device was added to your account and the activity of your account. The activity list tells you from which device you logged in before.
Make sure you choose a name which is know to yourself, because if somebody uses the same name it might confuse you.
Does it include the Facebook apps for mobile devices ?
Not sure. I tried a couple of time from Facebook app on my blackberry but it never asked for any device registration. I am guessing it only happens when you use a browser on your mobile or computer but not with the apps. So either it is not working for me or the apps need an update.
Update : When you login from mobile device, it does not ask you add that as device but only displays it as Mobile Device. So make sure you remember this part.
Looks for apps it seems to be sending emails with subject Facebook login using Facebook for BlackBerry® smartphones which is for Apps.