So, I just logged on to my computer today, in the way that anyone would log onto a computer, and I did nothing but boot up Fallout 3....and my saves were just gone. Nonexistent, and the saves folder in My Games was totally empty. It also was not in my trash bin. Is there a way I can recover my saves? (I have the GOTY, Steam version.)

That's weird. I assume that they aren't saved on steam's cloud service due to the age of the game. Have you looked in your game install folder?
You could try a number of free recovery programs (just be careful not to get something that might harm your computer) to see if they could possible restore something. If the data hasn't been overwritten by other processes, the saves should still exist on your drive even if they are deleted.

Also maybe you should consider an antivirus scan just to be sure. Files shouldn't suddenly go missing like that.

@DaltonMangum This could be a problem with Games for Windows Live feature. Have you ever used it? Do you have any other folders in My Games/Fallout 3 folder?
You can try disabling the feature with this mod: http://www.nexusmods.com/fallout3/mods/1086/?
Read the second paragraph in the description and see if you can relate to it.