As far as I know, when you go to any website or location on the web, it will transmit your IP address. The only way around this is to set up some type of proxy system where you are behind another computer that uses it's IP address for the internet instead of yours.
At our business, we have a gateway that uses one static IP address for a lot of computers behind the gateway.
There isn't much anyone can do with your IP address besides scan your machine for open ports/sockets. You might want to download a program that checks for open sockets and closes them.
One of the many ways a hacker can get into your machine is by sockets that are left open.