itunes wants my ID

When I open iTunes, a window keeps popping up to ask for my Apple ID. I have to click "cancel" at least twice, sometimes many more times, to make it go away. This is irritating, but much worse is when the window suddenly pops up when I'm in the middle of a podcast. In that case, it ends the podcast so that I have to find it again and figure out where I was when it stopped. I have this problem on both my MacBook Air and my MacBook Pro—although it only started happening on the Pro recently. Clearly, I don't need to have entered my Apple ID in order to listen to podcasts. How can I make this window stop popping up?