After many months in India I stumbled on my preferred method:

 * say nothing
 * give the palms together Indian greeting to the person asking as in the image below (they will almost always respond in kind)
 * continue with what I was doing

I do like that this is a bit more respectful to the other person.  However, the main advantage is that when I just ignored the person begging they would often continue following me and asking.  Every time I tried the above method they always moved on.  Works like magic.

![Clasped Hands](http://us.123rf.com/400wm/400/400/anandkrish16/anandkrish161202/anandkrish16120200013/12176460-greeting-indian-business-man-portrait.jpg)