I don't call Reservations very often, but I'd say that about half of my calls have been answered in the India call center.
The India call center is quite short-sighted, in my opinion. I've just sent a letter to UA. I documented the amount of my (generally quite high-yield) business that they've lost, as a direct result of their offshoring practices. (I still fly UA sometimes, mainly because they're sometimes the only practical option.)
CO doesn't operate any offshore call centers, and they indicate that they don't plan to do so either.
As far as I know, the LCCs don't operate offshore call centers either.