I've been having this problem and solved it. While I was looking for a fix, I've found that it is a common problem and the cause can be pretty much anything. I thought it would be a good idea to list potential causes for this problem for future reference. Feel free to complete this list if I've missed anything.
Here are some of the possible causes for iTunes starting up / playing songs by itself :
If nothing else works, you can try starting the Activity Monitor (under Utilities or System, not sure) and ending iTunes Helper process. This *might* solve your problem, as one of iTunes Helper's purpose is to start iTunes automatically when required. Ending it is not recommended as it is supposed to always be running in the background but it may solve your problem if nothing else works.