Corrupt font collection files is one reason Font Book will do this. If it's still running, Force quit Font Book. In your user account, open the ~/Library/FontCollections/ folder. Put all .collection files into a new folder on the desktop, or simply put them in the trash. This includes the default ones (Fixed, Fun, Modern, etc.). None of the defaults need to be there. They're just examples of how to use collections (font sets).
Launch Font Book. It should open. Assuming it does, quit FB again. Put some (not all) of your .collection files back if you'd prefer not starting over. Open FB. If it hangs, at least one of the collection files you put back is corrupt. You'll have to perform a loop of force quit FB, remove one collection, try again. Each time it hangs, repeat the loop until FB launches normally. You'll know the last collection file you removed is bad. Trash it.