The longest non-stop scheduled passenger flight is Singapore Airline's flight SQ21 between Newark and Singapore. It flies 16,600km (10,314 miles) in 18 hours, 40 minutes and crosses the North Pole. Because of the prevailing winds, the Newark - Singapore leg has different routing than Singapore - Newark. Singapore - Newark is 1,000 km and 2.5 hours shorter. The aircraft is an Airbus A340-500.
A list of the current longest flights is on Wikipedia here.