Possible cause 1: The Dock isn't responding.
Solution 1: Restart the Dock (log out then back in, or open Activity Monitor, find the Dock process, and quit it - it should auto-restart).
Possible cause 2: Something else not responding is preventing iTunes from opening normally.
Solution 2: Restart the computer.
Possible cause 3: Your iTunes preference file is corrupted.
Solution 3: Delete the preference file. It is located at ~/Library/Preferences/com.apple.iTunes.plist, where ~ is your home folder.
Possible cause 4: Your iTunes database file is corrupted.
Solution 4: Move the database file elsewhere - it is located, by default, at ~/Music/iTunes/iTunes Library (this location can be changed), then relaunch iTunes.