There are a few things that can cause iTunes to start playing seemingly 'without cause'
Here's a few I know about:
1. If you are on a mac with an infrared (IR) sensor, then a remote (either for a Mac or for an Apple TV) could be causing your mac to play (this was my case - my computer was receiving the "play" command from the Apple TV remote when my mom played or paused a show on the Apple TV.
2. If Home sharing is turned on (on Windows or Mac), then some device (like an iOS device) could be giving the computer the command to play via the WiFi network. Disabling Home Sharing from Settings should fix this problem.
3. The 'play/pause' button on your keyboard could be malfunctioning. If you're using a desktop computer, changing out the keyboard may fix this problem. If you have a laptop, that's a little more difficult. If it's a Macbook you should take it to the Apple Store and see if they'll fix the button for you.
There are probably other problems, but I thought this might help some people.
Hope that helps and God bless!