How to fix iTunes/Skype where fonts all show up as boxes after Mountain Lion upgrade?
This usually happens when you have Fonts Caches (or actual Fonts) that are corrupt. I would do the following, to not only clear the caches, but also to verify your Fonts.

Clearing the font cache - you have a few options (Onyx is just easier).


Use a tool like Onyx, which can do this and many other maintenance tasks for you.
Manually remove the cache with the command line atsutil utility. You basically would do astutil databases -removeUser then sudo astutil databases -remove, then astutil server -shutdown, then astutil server -ping. I would recommend restarting after this.
Choose from various other utilities like Onyx that clear just the font cache. 
Some people also recommend clearing out the /Library/Caches folder, but I am not sure how well this works. There also used to be some older ways to clear the cache but I cant find them (and I am pretty sure it was tools before Mac OS 10.5). 


Verifying Fonts


Open up Font Book (in /Applications/)
Select All
Go to the File Menu and select Validate Fonts. 
Resolve any issues this may present, but those may be specific to your machine.




Usually clearing the Font Cache works. I used to see a similar problem all the time with Microsoft Office 2004, and it had its own cache that we even cleared weekly. I haven't seen the Mac OS mess its cache up that often, but when it does, usually a quick fix. I have even seen a reboot sometimes clear it up (in very minor cases).