I am a programmer, paid hourly. My workplace recently added a gym to its facilities. If I use this gym, should I count it in my hours worked, or discount those hours when reporting?
Almost assuredly no.
If there is a liberal policy like foosball tables in the work area so creative people can blow off steam while their minds chug in the background, then maybe. But you are spending time on something that has no outwardly visible resemblance to your work. In so doing you are at minimum inviting questions. By the time it comes to the point of someone asking the question, you can also rest assured they're already annoyed and you're starting your explanation from inside a hole.
If you are set on doing it, I'd at least start with asking your manager. edit: And if you do, ask the question in a fashion indicating you very much do not expect it to be considered work time.
No. Company provided or not unless your work directly involves working out, it would not qualify as working hours. If anything, your employer is providing you with a resource that is otherwise something that would come out of your pocket as a monthly expense.