iTunes run!

Check Dashboard to see if you have any iTunes-related widgets running. If so, close them and see if that makes a difference. Similarly, look for any third-party apps that may be related to iTunes, such as apps that copy "now playing" information to a web site.

Another possibility is external speakers, if you have them. Another user here found that a loose speaker connection may cause random launching and playing on iTunes. Try wiggling the speaker plug and see if that causes iTunes to launch. If so, unplugging and reconnecting the speakers may cure the problem. If not, you may have a defective speaker jack or an off-size plug on the speakers.

Hope this helps.