I depends. If you use credit cards, subscribe to magazines, were born in a hospital, go to a doctor, have a bank account or loan, pay bills, or any number of other mundane, ordinary activities, the government (or practically anyone for that matter) can find a substantial amount of your personal information. OTOH, If you have no birth certificate, always deal in cash, never obtained a SSN or drivers license, don't receive mail or own a phone, no electricity or municipal water, etc., the government probably does not know you exist.
The bottom line, though, is that the government does not know how much it knows about you. There is no master database. Governments work mostly as independant departments and information links between departments are virtually nonexistant. Don't sweat Big Brother just yet.
The overwhelming majority of people have more than the average (mean) number of legs. -- E. Grebenik