– Finding the cause, not the fix
Most of the work I did at Apple and do at my current job when confronted with a problem was not trying to fix the issue. The real helpful part is finding where the issue is.
OS X has an easy time rebuilding files that it needs. More often than not, removing the problem files will result in the OS automatically re-creating a fresh copy of the file without any issues. Finding these files is not too hard. Just narrow it down. As always, do a backup of everything incase you accidentally delete something that was more necessary than you might have thought.
– User or System
Almost all software issues fall into problems with files within the User or System folder. A very quick and easy thing to try is to create a new user and see if the same issue you’re having is happening there.
If it does, you’re dealing with an issue with something in the Application or System folders. Try re-installing the App or the  OS. (Please backup first!)
– Libraries or Library
If your issue doesn’t happen in the new user, you’re problem is in your User folder.
A few apps, like iTunes and iPhoto have Libraries that might prevent the app from opening. In either of those apps, press and hold down option when opening the app. This will allow you to create a new blank library. If that blank library doesn’t seem to have the same issue as the main one, your problem is probably there. (Press and hold option again and choose your old library.)
All apps create a file on your Mac that keep track of how you like things setup. (Window size, customized settings, etc…) It isn’t uncommon for this Preference file to get messed up to the point of causing issues with the App. To find it, open the Library. Open the Preferences folder and find the App in question. (It will be named in the following way: com.company.app, for instance, com.apple.iTunes) Move that file to the desktop (backup!) and remove it from the Preference folder. Open the app and see if it works. If not, but the backup file back.