Does anyone know how to get a cat to use the litter box when he prefers the
carpet, or even the floor?  He was rescued as an adult tom cat (unneutered
male) that had been abandoned outdoors, and he was in pretty bad shape.  He
loves being an indoor cat now, and he's been neutered, but he's very
inconsistent about his litter box habits.  Help, anyone?

I had the same problem as well as a friend of mine.  What I did was get a
large under-the-bed rubbermaid container and filled it with a good amount
of litter.  This did the trick.  The problem with many litter boxes are
they are too small for the cats and they like the bigger ones. This really
worked for the both of us and now that is all my cat uses is the rubbermaid
under-the-bed box and has not had a accident out of the box since.
You may just also rule out a blockage from Kidney stones if this does not
help.  

You're a genius!!  Thanks so much for the suggestion, it appears to be working!