The record for the longest non-stop commercial flight is currently held by Singapore Airlines for its flght routes from Singapore to New York and los Angeles. The business class only journey to New York's Newark Airport takes nearly 19 hours and is over 8,200 miles long. The LA flight is slightly shorter, but still over 7,600 miles and taking over 18 hours.
However, both these routes are due to be closed by the end of 2013 as the cost of running them is too high and the take-up for business class flights is no longer as high as it was. Singapore Airlines will of course continue to operate plenty of commercial flights to the US, but these will include stop-offs.
After 2013, the longest such flight will be the Sidney to Dallas route operated by the Australian airline Qantas. This is a 15 1/4 hour flight over a route of 7,400 miles.