The Federal Anti-Money Laundering (Federal AML) impose regulations which Stripe abides by. In addition to the federal regulation, Stripe follows "Know your Customer" (KYC) guidelines.
Stripe is required to meet the compliance laws in all 135+ countries in which they operate. Depending upon where you are signing up from, different types of information will be requested by Stripe. This is to help countries and governments fight tax fraud and money laundering.
More information on the type of information Stripe may ask from you for verification purposes can be seen on this page.
Please note, Stripe only asks for the last 4 digits of SSN for US-based customers.