Here's a list of what you definitely need when you go to sign up for Obama Care AKA Covered California:
Annual income for 2014
Social Security Numbers
Dates of birth
Naturalization Number or Alien Number for people born outside of the US
Here is a list of Documents that are sometimes needed:
Proof of Income (Pay Stub, W2, 2012 Taxes)
Proof of Residency (CA Driver's License, Bills)
Proof of Citizenship (Passport, Birth Certificate)