Some of the Airlines flying into India:
Air India
Jet Airways
Air France -- via Paris
Alitalia -- via Rome
British Airways -- via London
KLM -- via Amsterdam
Lufthansa -- via Frankfurt
Swiss Air -- via Zurich
American Airlines -- via European Gateways
Continental -- via European Gateways
Delta -- via European Gateways
Northwest Airlines -- via European Gateways
Cathay Pacific -- via Hong Kong
Eva Air -- via Taipei
Malaysian Airlines -- via Kula Lumpur
Nippon Airways -- via Tokyo
Singapore Airlines -- via Singapore
Emirates -- via Dubai
Domestic Airlines (full service):
Indian Airlines
Jet Airways
Kingfisher Airlines
Domestic Airlines (low cost):
JetLite
IndiGo
SpiceJet
GoAir
Useful sites for domestic travel (can compare fares and buy tickets):