It all depends on what you want to mask your IP from.
You can't just change your ip, it has been assigned to your by your isp, weather permenant or leased for 2 hours (eg dialup) or more.
The simple fact is that it's impossible to genuinelly hide your ip, you can hide it from websites, IRC servers, Mail servers, and so on, but even then all you're doing is using someone else's computer, therefore passing YOUR ip to a second computer, and the second computers IP to the server you are connecting to.
Someone having your IP is NOT a security risk (woo, how many people are gonna correct me on this.....), unless you are running some sort of service or deamon, then they're not going to "hack" you or anything like that, they may try DoS/DDoS, but thats only if you've pissed someone off, whereby, you deserve it.
I'm just tired of paranoid people. bleh.