I think somebody logged into my Facebook account. Is there any way for me to find the last login IP address or the location from where this occurred?
You can configure Facebook to always ask you to register the device whenever you log in to a new location. It then shows a log of where you have recently logged in from. Note that when you log in it asks you to choose the location name yourself, so it's possible that an attacker could get a lucky guess as to what you would set it to yourself, but this can help determine if people might be accessing your account without your permission.
To enable this setting, click on the Account dropdown in the upper right, then click Account Settings. Then click "manage" next to the Security section. There you can enable tracking and see where you've logged in from and when.
Since I originally posted this answer, the tool has been updated, and now shows the location you last logged in from, based on GeoIP. If you hover over the estimated location, it will tell you the IP associated with that login. It will also tell you what type of device you were logged in from, for example, chrome on Windows 7. You can terminate any other sessions which may be unauthorized activity.
You can get a list of the sessions that are currently logged in to your account. From the Account menu in the upper right corner choose Account Settings, then click the Account Security change link. This shows the current logins, including IP address if you hover over the location, and will even allow you to log out other sessions. However, if the other session has logged out then it does not appear.
Also under Account Security you can turn on notifications if a new computer or mobile device logs in to your account, but that won't help with prior logins.
If there is activity from an unexpected (far away?) location, Facebook does track that and may ask you to answer some questions to confirm your identity.
Actually, we can see the IP address, browser client type, time date, and location of our last login
Here is what I found:
Login to Facebook and click on “Account” dropdown menu on the top right corner of your screen. Click on “Account Settings”.
You will be taken to the Facebook “My account” page, where you will a number of tabs, each account for settings for different sections of Facebook. Click on Settings tab.
Find the “Account Security tab “under settings, you will have the account activity details listed under “Most Recent Activity”
You can find the last accessed time, location and the device from where your account has been accessed. You can even enable SMS or email notifications whenever your account is accessed from a new computer or mobile device, just select “On” radio button under “Login Notifications” and click Save button.