Nothing except your name and the phone number. When you call to report it lost or stolen they will ask for the last 4 digits of your SS#. I had to call and report my husband's sync lost last week. It was very easy.
It also helps to have the IMEI number of your phone, you will find this on the box. If you are on a GSM network (T-Mobile or AT&T) the thief will still be able to use your phone, they just simply need to put in a new SIM card. Most carriers will not do anymore than deactivate your SIM card which will make it so your are not charged for calls, data usage etc, however it will not get your phone back.
For your next phone you might want to look at GadgetTrak PhoneBak ( http://www.gadgettrak.com/products/phonebak ). When the thief removes your SIM card and inserts their own, the software sends SMS messages to pre-defined numbers (spouse etc) with the new number as well as subscriber IDs which you can provide to law enforcement to follow up with and get your phone back...as well as catch the jerk who stole it. No iPhone support yet, but it is coming.