What are the busiest airways?
You can use Flightradar24 which will shows air traffic in real time where you can check which airlines are the busiest. Flightradar24 is using the callsign of the flight and compare it with big databases of airline and airport schedules to find the matching flight number, so not all airlines are submitting their schedules.

You can choose Airline fleet database in Data/History where you can check a comprehensive guide about the fleets of the world's airlines. Once you select an individual airline to view, you'll get its entire fleet. However it won't give you exact number, but list of all airplanes flying per airline (e.g. EasyJet).

To display the number, either you should request that information from the author of the site, or there are few workarounds.



Technical analysis of the busiest airline

When you open the page with specific airline (as suggested above, e.g. EasyJet), you can type the following command in JS console (e.g. in Chrome - More tools and choose JavaScript Console):

$("#listAircrafts li").length


and it'll print you the number of flying planes (sometimes less, because of the pager).

Or use Yahoo Developer Console and type the following query:

select * from html where url="http://www.flightradar24.com/data/airplanes/ryanair-ryr/" and xpath = '//*[@id="listAircrafts"]/li'


And in Tree View, you'll see number of flying planes at the moment (e.g. count: 323) based on Flightradar24 database.

To combine all lists together, you need a script as below.

In example the following *nix command (it'll take few minutes to run):

$ time for uri in `curl -s http://www.flightradar24.com/data/airplanes/ | grep -o 'data/airplanes/.*-[^"]*'`; do curl -s http://www.flightradar24.com/$uri | grep -o '/data/airplanes/.*-[^"]*' | wc -l; echo $uri; done | paste -d" " - - | sort -nr | head -n20
521 data/airplanes/airbus-aib/
484 data/airplanes/china-southern-airlines-csn/
411 data/airplanes/china-eastern-airlines-ces/
404 data/airplanes/lufthansa-dlh/
341 data/airplanes/air-china-cca/
324 data/airplanes/ryanair-ryr/
306 data/airplanes/british-airways-baw/
259 data/airplanes/turkish-airlines-thy/
254 data/airplanes/air-france-afr/
246 data/airplanes/emirates-uae/
214 data/airplanes/easyjet-ezy/
193 data/airplanes/saudi-arabian-airlines-sva/
186 data/airplanes/air-canada-aca/
184 data/airplanes/air-berlin-ber/
179 data/airplanes/netjets-nje/
176 data/airplanes/aeroflot-afl/
171 data/airplanes/qantas-qfa/
169 data/airplanes/tam-linhas-aereas-tam/
163 data/airplanes/cathay-pacific-cpa/
157 data/airplanes/sas-sas/


It will scan over 800 different airlines from the web and it'll print sorted list of the 20 busiest airways according to Flightradar24 database at the time of scanning. Tested on Linux and OSX.



Technical analysis of the busiest route

In order to calculate the busiest city to city routes, it's more complex that above example and you'll have to write similar script (or spreadsheet) of fetching all departures/arrivals of each airport (e.g. LGW) from available Airport database over world airports page, extract data from the tables, consolidate the airport/destination and sum it up in similar way.

Example extraction from table for LGW airport:



Extraction formula which I've used to list all departures from London Gatwick in Google Spreadsheet:

=ImportHtml("http://www.flightstats.com/go/weblet?guid=34b64945a69b9cac:4bf2fb3c:1246346ea7d:4597&amp;weblet=status&amp;action=AirportFlightStatus&amp;airportCode=LGW&amp;airportQueryType=0%22", "table", 0)


So theoretically you can extract all departures of the airport per Sheet (it's like over 3000), group Destination (so you know at least the busiest destination per airport) and sum it up, do some consolidation between Sheets plus some magic, and viola. That's why it's better to write some script:) If I'd have too much time on hand, of course I could do it.

So in other words, the busiest air route would be the airport which will have the highest number of the same Destination city (if I'm correct).

You can always simplify the work by choosing top 20 airports to give you some idea how does it work (instead of checking all of them).



Conclusion

Maybe it won't answer your question directly (which route is the busiest), but it's an idea how to extract the data of the busiest airlines and similar statistics. As it seems it takes a bit knowledge and time how to do it.

If you find any easier way of extracting that data or different database, let me know:)



Summary of the busiest airline

So based on above data (and ignoring Airbus), it's:

18:00 UTC/GMT (Friday)


China Southern Airlines (484)
China Eastern Airlines (411)
Lufthansa (404)
Air China (341)
Ryanair (324)
British Airways (306)
Turkish Airlines (259)
Air France (254)
Emirates (246)
EasyJet (214)


The data is indicative and it depends on the time of day and week, so I'm not warrant of any correctness of it as this is only the example.