Every computer connected to Internet is given a public IP address. As you surf online, that IP address is recorded in log files kept on servers. Your Internet activity can be used against you — no matter by whom, by the police or hackers. This is not to mention the fact that anyone in the Net can determine your real location — country, state, town, street, and even house and apartment number.
So it will be better to hide your real IP address and make your surfing — and life — as anonymous as possible.