I've made a list of grants that a computer scientist in India can apply for. Many of these will be eligible for other disciplines as well, especially engineering. I found a couple of good lists: here and here. But these were still not comprehensive so I made my own. Do email me if you find any new ones.

Faculty Awards:
  1. IBM Faculty awards
  2. Google Faculty award
  3. DST FastTrack award
  4. Swarnajayanti Award. Applications due: May 15, 2015.

Travel Grants:
  1. SERB.
  2. IARCS.
  3. Centre for International Co-operation in Science.
  4. Ratan Tata Trust.

International Collaboration Grants: Not all grants are active at all times but below are some that are recurring. Some of the links below may refer to past deadlines, but these are worth bookmarking and checking periodically.
  1. Indo-UK
  2. Indo-Israel. Search for ISF-UGC. Due early Nov.
  3. Indo-French. This is the link for the collaborative research project.
  4. Indo-US

For Students:
  1. Anota Borg awards
  2. TCS Research Scholarship.
  3. IBM Ph.D Fellowship.
  4. Facebook Fellowship Award.