If you were one of those (as I was) who followed the hint regarding session-only cookies in Safari, then you are possibly still being prompted for your password in iTunes, at least in Lion.
I discovered, after trying every hint I could find without success, that if the user permissions for ~/Library/Cookies/ is still set to read only for the user, then you will still be prompted for your password the first time you activate iTunes after a login.
The file, ~/Library/Cookies/Cookies.binarycookies is not being created/updated.
[crarko adds: I haven't tested this one. It seems clear if a user doesn't have write access to a directory in their own Library it could cause problems like this. If somebody who has used the previous hint mentioned and is still on 10.5 or 10.6 can comment on whether they are affected by this, it would be appreciated.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20111221134258613