A friend in San Francisco is trying to figure it out, given that there are (apparently) nonstop flights to Dubai, it should be physically possible, but wondering if such flights exist?
The earlier accepted answer by JonathanReez was written in 2014. From December 2015, Air India operates a San Francisco - Delhi flight.
As of 2014, Singapore Airlines Cargo provides a cargo flight from Los Angeles to Mumbai. Otherwise no such flights exist from LAX, SFO or YVR (the only likely candidates).
As of 2015, a new flight has opened up between San Francisco and Delhi, as correctly mentioned above.