This was cross-posted on Cloudburst Mumbai.
Uma has some information here about where to go to donate old clothes, but I'd make careful enquiries before donating any, if I were you. When I travelled through the tsunami-affected areas of Tamil Nadu in January this year, one of the common themes I encountered was how donating clothes was a waste, and how no one wanted them and they would just form colourful heaps of garbage on the sides of roads. (And we have enough of those already.) I wrote about it here and here, and Dilip D'Souza, who travelled with me, mentioned it here and here.
One of the main reasons these clothes go waste is that their intended recepients are not beggars, but proud people hit by circumstances who don't necessarily want old, faded hand-me-downs, which are also sometimes inappropriate given the kind of lives they lead. However, if the NGO concerned is making an effort to make those clothes presentable and acceptable to those they are intended for, as the Rotary Club of Chennai did after the tsunami, then it might be worth it. Otherwise they will just end up piled up on the streetside.
Gaurav brought this subject to my attention now, and has posted about it here.