What is the longest passenger flight (with a flight number) in the world?

From Wikipedia:

Newark - Singapore (Singapore Airlines)
flight number: SQ 21,
15,345km (9,535 miles, 8,285 nautical miles)
from 18 hr 40 min to 18 hr 50 min,
aircraft: Airbus A340-500,
first flight - 29 June 2004

Second place:

Los Angeles - Singapore (Singapore Airlines)
flight number: SQ 37,
14,114km (8,770 miles, 7,621 nautical miles)
from 17 hr 20 min to 18 hr 05 min,
aircraft: Airbus A340-500,
first flight - 3 February 2004

Third place (surprisingly only by distance, but not by time)

Sydney - Dallas (Qantas)
flight number: QF 7,
13,804km (8,578 miles, 7,454 nautical miles)
15 hr 25 min,
aircraft: Boeing 747-400,
first flight - 16 May 2011

Third place by time:

Los Angeles - Bangkok (Thai Airways International)
flight number: TG 795,
13,309km (8,270 miles, 7,186 nautical miles)
17 hr 20 min,
aircraft: Airbus A340-500,
first flight - 28 September 2006

The longest flight by flight number (including stops) would be Korean Air's flight 062 from Guarulhos Gov Andre Franco Montouro (GRU) in Sao Paulo, Brazil to Incheon Intl (ICN) in South Korea via Los Angeles International (LAX). It is 28 hours and 35 minutes.

Since the two answers so far will no longer be valid soon, I thought it is time to add a new answer:

Singapore Airlines is cancelling their nonstop flights from Newark to Singapore and from Los Angeles to Singapore. So the longest flight will be Sydney - Dallas by Qantas (QF7).

According to this CNN article, the record has been broken because of the COVID-19 outbreak:

On March 14, French airline Air Tahiti Nui flew the longest ever scheduled passenger flight by distance -- transiting 9,765 miles across the world from Papeete, in Tahiti, French Polynesia, to Paris' Charles de Gaulle airport.

This one off milestone was a direct consequence of the coronavirus-induced US travel restrictions.

This route usually involves a scheduled stopover at Los Angeles International Airport (LAX). But when an airplane stops over in the US, all passengers must alight the aircraft and proceed through US Customs and Border Protection before they're allowed to advance on with the next leg of their journey.

Current restrictions rendered this part of the journey untenable, so instead, flight TN064 just carried straight on, departing at 3 a.m. local time from Papeete airport and arriving in Paris at 6:30 a.m. local time on March 15.

This is a scheduled flight, but a one time deviation from the schedule (though the situation may continue to be like this in the near future).

Air India Flight 173 from New Delhi to San Francisco is the world's longest flight. It covers over 15,000 km (9,300 miles) en route, over the Pacific Ocean in about 15 hours.

This is from Flightaware:

_{(source: quoracdn.net)}

The Wikipedia page has now been updated as well.

Since 15 October 2016, Air India Flight 173 from New Delhi to San Francisco started flying over the Pacific Ocean. Tailwinds over the Pacific Ocean helped in reducing the flight time by 2 hours, despite increasing the total distance by 1,100 km. This also made AI 173 the world's longest flight by actual distance flown, with total distance traveled being over 15,100 km (9400 miles).The return flight AI 174 however still flies over the Atlantic Ocean, to take advantage of tailwinds in that direction. Air India therefore advertised this route as around the world flight, as it departs over Pacific and returns over Atlantic.

Some other interesting articles and videos on AI 173:

1. Air India taking advantage of tailwinds

2. Air India now operates the world's longest routing (sort of)

3. Official statement by Air India captain Rajneesh Sharma

Here is an update for 2016:

Early on 3 March, Emirates flight 449 made history when it touched down in Dubai from Auckland. The Airbus A380 covered an estimated 9,000 miles between New Zealand’s largest city and the airline's hub, making it the current longest non-stop scheduled commercial flight by a distance.

The Independent

Here is what we can look forward to in the coming years:

Qatar Airways Flight 921 from Auckland to Doha, which will be the longest flight in the world, will be flown with a Boeing 777-200LR when it starts 2 February 2017, overtaking Emirates' spot with their Auckland-Dubai flight. Wikipedia

Singapore Airlines revealed plans last year to bring back its Singapore-New Jersey service in 2018. The flight will apparently cover some 15,300km (9,500 miles) in 19 hours.