Even if you don't give away your IP address it still CAN be found by those malicious idiots out there who think that trashing computers is cool.
And because whenever you connect to the internet your computer is like a postcard ready to be read by anybody who bothers, you ought to find particular ways of protecting it if you haven't already done so.
E.G Get a decent firewall -like BlackICE Defencer (not Zonealarm..biut that's personal taste), or get McAffee's latest firewall.
Also, consider using a way of connecting to other people's public permissable servers that are 'anonymous' whenever you can, although finding a good, speedy and flexible SOCKS server can be very difficult these days (for free), but do a few online seraches, or just be prepared to pay for specialist privacy software, etc.
Anyway, hope that's of some help to you.
Be carefl, in the world of computer tech there are plenty of fools out theree ready to prey on unsuspecting users.