You could create a multiplayer-like game using PHP, MYSQL and AJAX.
The concept is to store the players information (x and y axis, and possible their angles?) inside a MYSQL database.
In order to achieve this, you send an AJAX post to your webserver with a PHP file posting the current position of player and their angle to a MYSQL database.
On the other hand, you can call an AJAX request to a PHP file bringing in the new values of players x and y axis and their angle, giving the multiplayer-like effect.
This coupled with a simple login feature, you could have the basis for a simplistic online game.
As you said Facebook, using the Facebook plugin feature, you can store the players Facebook ID, which is unique and you can use that to store a players information.
Example:
ID: 1 (primary key, auto increment)
Player ID (Facebook ID) (unique key)
X_Position: 650
Y_Position: 190
Angle: 90
The above could be your MYSQL database layout.