So, on my PC I use AbiWord for word-processing since I'm too cheap for the Microsoft Office stuff.  Ordinarily it just has .rtf and .doc files and the like associated with it, but for some reason, Abiword is trying to open .exe files like ctfmon.exe!  Is there some way I can change the association for .exe files so they open normally or do I have to reinstall here?

have a look here
 
and
 
here
 
now I understand that your problem isn't that you can't open exe files but that abi opens them.
 
the problem is that either by mistake you associate exe files to open with abi or a virus did that for you.
 
so make sure you got an upto date anti virus run a check and if your system is clean then follow the fix from the 2 above links since the same fix applies to you  good luck

None of those worked for me, but I seem to have fixed the problem by creating a new user account and moving my settings there.
 
And yeah, it was my fault   .  At least that means it wasn't a virus ...

well glad you got it sorted out