I contacted PayPal to let them know that I'm not okay with them demanding my Social Security Number when there is no law requiring them to do so (and because I now trust them about as much as I trust Halliburton, Tyson, Monsanto & Pfizer).

Here are the replies I received:

First reply:

Due to Regulatory requirements all financial institutions (like PayPal) have to collect sender’s identifying information, such as Taxpayer Identification Number when making certain payments. By providing this information you are helping PayPal to get to know you better and increase the overall security of our community.

You may choose to not provide the information, but you will be unable to continue with money transfers. Once you have provided the necessary identification information, we will keep your information on record to be used for future qualifying payments.

The privacy of your personal and financial information is something we take very seriously, and we use your information only in accordance with the terms of our Privacy Policy.

Your information is protected by high standards of security, such as firewalls and data encryption, and we’ll never reveal your financial information to anyone, unless we have your express permission to do so, or if we are required to do so by law.

To learn more about the ways we protect, collect, store, and use your personal information, please view our Privacy Policy. To view our Privacy Policy, click the Privacy link at the bottom of any PayPal page.

If you feel that your concern was not completely resolved, please let us know. Thank you for being a valuable member of the PayPal community.

Second reply after I questioned the legitimacy of the claims in the first:

I understand your hesitation to provide your SSN. Let me assist you with this email.

It is optional for the customers if they want to provide the SSN. This is part of the Patriot Act and we must comply with its requirements. This information also helps us keep the PayPal community safe. Due to recent changes in the Bank Secrecy and Patriot acts, we are required to gather information on our customers in order to allow use of some of our products. To comply with these regulations, we must implement a Customer Identification Program (CIP) and verify the identity of our customers.

CIP requirements might vary by region, but will include the customer name, home address, date of birth, and Social Security Number (SSN). If we are unable to verify the CIP information, we cannot provide certain services and may have to place a limitation on the PayPal account.

If you still want to close the account, please follow the steps below:

Log in to your PayPal account.
Click the Business Profile icon next to "Log Out" and select Profile and settings.
Click My settings.
Click Close account next to "Account type."
Choose up to 3 reasons why you want to close your account and enter any additional information.
Click Continue.
Click Close Account.

For further assistance, you can contact us at 888-221-1161:

• 4:00 AM PT to 10:00 PM PT, Monday–Friday.
• 6:00 AM PT to 8:00 PM PT, Saturday and Sunday.

We appreciate your understanding. Thank you for your time and patience.
So, it appears to me that they are not legally obligated to demand a SSN but rather are obligated to establish a Customer Identification Program (CIP) to ensure that there is a real-word identity associated with each PayPal account, and it is PayPal alone (not the corrupt federal government) that is choosing to demand a SSN even though the personal information they previously demanded was more than sufficient for verifying the identities of PayPal account holders.
My guess is that they want to demand SSN numbers for three primary reasons:
1. They believe they can get away with it.
2. More information = more power. They can do a lot more in-house, including (but certainly not limited to) checking users' credit history.
3. People will start to regard them more as an actual bank rather than just a money transfer service.