Somehow I managed to download a version of Arduino that doesn't include the Wire library. Yeah, I don't understand it either. Anyway, does anyone have a link to where I can download that library?
Download the IDE again. Do it right this time. 
The download and install process is basically foolproof. There aren't any choices you can make to mess this up.
So, instead of re-installing, try this:
Click the Sketch menu, Import Library, Add Library ...
browse to a folder like this:
c:\program files (x86)\Arduino\hardware\arduino\avr\libraries
Click the "Wire" folder and click Open.
If you go back to the Sketch menu, Import Library, Wire should be on the list now.
Good luck!