Thanks all for your reply!
@fabl: I have used ArcMap and ArcCatalog, still no luck. I have not tried exporting the tiffs to another format, but will look into this. I would rather not go down this route since I have a large collection of images.
@sachin.kanaujia.gis: The tiffs have world files, statistics files and pyramid files that accompany them. The tagviewer application you suggested does not show any corrupt tags related to the .tif file itself.
@Eric: I am on 10.1. I have had another team member on 10.1 attempt to assign the projection and still no luck. We all have the proper premissions on the data files, so I don't believe that is the problem. This issue applies to all .tif files within this collection of imagery. I can't remember the last time I've had to assign a projection to an imagery file, so I can't remember if I have performed this operation in 10.1 before. I will have a look at assigning the projection using a 10.0 machine and see if I have the same results.