Steering on my 2001 is getting tighter and tighter (less play). I've actually loosened up the adjustment nut on the box (turned counterclockwise). Is this a symptom of the box going or some other problem???

 

Check the column - I went through this on my truck a while back. Bad column bearings.

 

Also check the steering rack (check the boots to see if they are torn and the rack is rusted etc.) and the upper and lower ball joints to see if they are binding. It could be the power steering pump or fluid.
Definitely check the steering column also like bill said but before playing with that disconnect the battery to disable the air bag.
I could just be a simple thing.