On Form I-821D, you are asked to provide your "social security number." On Form I-765 (the work permit application) you are asked to provide all social security numbers you've ever used.
A lot of people are concerned - rightly so - with this question: "If I used a fake SSN, should I put it down on the forms? And if so, how?"
UPDATE: As of 9/14/2012, USCIS has indicated that when they ask you for a social security number, they are asking about real, valid social security numbers only. That means if you've used a fake one, you do NOT need to put it down.
The original posting has been deleted to avoid confusion.
Read about how to get a social security number right here.