Repaired permissions with Disk Utility?
Try starting iTunes with the option key held down and have it create a new library as a test. If that works you may need to rebuild your old library: How to re-create your iTunes library and playlists - http://support.apple.com/kb/ht1451
Try moving the Genius file in your user library to another folder and start from your normal library (hold down option key, guide to your usual library). See also below about Genius issues.
Try starting iTunes with the shift key (command+option on some versions) held down which disables third party plugins. If it runs under these conditions then you probably have a conflict. iTunes: Troubleshooting issues with third-party iTunes plug-ins - http://support.apple.com/kb/TS3430
There are various iTunes preferences files that can be isolated to test if they are creating the problem.
Maybe: "iTunes quit unexpectedly" - https://discussions.apple.com/thread/3487024?answerId=16950029022#16950029022 - disabling Genius or even just restarting airport (https://discussions.apple.com/thread/3768917?answerId=17715416022#17715416022)