Most certainly to low, GitHub has over 1 million users alone. https://github.com/blog/455-100-000-users

I believe TCS, a large indian offshore company, employs over 100K programers (http://en.wikipedia.org/wiki/Tata_Consultancy_Services)

It depends on your definition. Something like one in a couple thousand is probably reasonable, or a few million.

If we're talking competent and capable of independently producing professional-grade output, you'll see another reducing factor of around 1:100 or more...so already down to a few tens of thousands. Once we start breaking that down into subfields like data mining or computer vision, the number of people in the field can get rather small.

But the question was number of programmers, Not in any particular sub-domain. Theoretically, even mathematicians can be called as programmers, only that they deal in Language called as Mathematics

The question was overly vague, which is why the first thing I said was "it depends on your definition." The broad estimate is on the first line.

How long is a piece of string? :)

[IMHO, it is the hackers who keep the world/universe going, because they are the ones who cause chaos/disruption (in absence of which, the 3rd law of thermodynamics would fail, causing the universe to implode).]

I've heard figures bandied about a few years ago implying there were about 12 million.

Employed programmers - 5 million. I saw some research done by a startup for their VC.