Apple tends to nag you if you're on a PC and don't have itunes, which I don't. At first, I thought this was an Apple trick to get me to sign up. Seriously.
I did take the steps to change my password, though, going directly to the Apple site to do so... but I've not gotten a response back with a confirming link to click on... and I'm continuing to get notices that someone/something is signing into various Apple services using one of my email addresses and an iPhone which I don't have.
Again, no response from Apple, so perhaps some cause for concern that someone is playing with my account. Haven't yet found an update on the story. Reports say they've fixed it, but I'm not seeing that.