(Revised and updated in February 2017).
In 2015 Emirates announced the advent of what would be the world’s longest non-stop flight between their Dubai hub and Panama City with an estimated flight time of over 17 hours. That service has not started yet. The current longest service (in km) is the Qatar Airways flight between Doha and Auckland, which is 14,534 km.It is scheuled at 17 hours 40 minutes. Details of these and other long hauls are given here: https://en.wikipedia.org/wiki/Non-stop_flight#Longest_flights
Note that the Delhi-San Francisco flight over the Pacific may turn out to be somewhat longer than 14500 km although the time taken is less than 15 hours due to tailwinds. It has once flown 16980 km in 14 hours 5 minutes.
This made one wonder which would be the longest non-stop flights within India. There are numerous websites where the great-circle distance can be found merely by feeding in the airport codes, such as: http://www.gcmap.com/
This site also gives details of the actual distance flown which will be more than the great-circle distance which is the theoretical minimum: http://uk.flightaware.com/
We get these as the four longest non-stop flights wholly within India:
(This has been updated with the inauguration of the Delhi-Thiruvananthapuram non-stop service by Indigo in January 2016)
Delhi-Thiruvananthapuram (DEL-TRV): 2224 km great circle, actual 2301 km, time 3 hr 20 minute (scheduled)-one pair of flights by Indigo daily.
Mumbai-Guwahati (BOM-GAU): 2073 km great circle, actual 2207 km, time 2 hr 55 minute (scheduled)-two pairs of flights by Indigo daily.
Delhi-Kochi (DEL-COK): 2040, 2112,3:10
Bengaluru-Guwahati (BLR-GAU): 2036, 2113,2:45
As you can see, scheduled timings depend on wind and other factors so the DEL-COK flight ends up taking slightly longer than the BOM-GAU flight.
There are various multi-leg flights which are longer: Delhi-Kolkata-Port Blair (1315 + 1301 = 2616) and Dehradun-Delhi-Bengaluru-Thiruvananthapuram (207 + 1703 + 529 =2439 km). A single-leg flight on these routes would be 2480 and 2407 km respectively, which should be technically feasible but would not attract enough traffic to be economic.
The same article also gives details of the longest flights for different aircraft models as well as airlines (though it does not include Spicejet and Indigo): https://en.wikipedia.org/wiki/Non-stop_flight#Longest_flights
You can also look up the shortest flights, in https://en.wikipedia.org/wiki/Non-stop_flight#Shortest_flights which tells us that the shortest scheduled airline flight is 93 km between Mumbai and Pune, operated by Jet. There are scheduled helicopter flights in the North-East operated by Pawan Hans which may be shorter.
In the Dakota age, there were some legs operated by Indian Airlines which were less than 50 km, as summarized in: https://abn397.wordpress.com/2015/06/27/a-slice-of-history-indian-airlines-in-1972-and-the-tripura-hopper/
which mentioned one sector in Tripura which was 21 km long.
Here is a news item about the DEL-TRV flight: