It's a bit hard to determine "City to City" as some places have 2, 3, 4 or more airports. As far as single airport to single airport routes go MEL-SYD is one of the top two in the world - something like 80+ flights per day in each direction.
The most popular US domestic routes are New York City-Boston, New York City-Miami, New York City-San Francisco, New York City-Los Angeles, and New York City-Chicago, along with Honolulu-some Haiwaian city I forgot. All six are among the ten busiest domestic routes in the world. Melbourne-Sydney is also on the TOP 10, and the other three are domestic Japanesse routes (Tokyo-Sapparo is number one, I think). Among the busiest international routes from the US, the three busiest are New York/JFK-London/LHR, Honolulu/HNL-Tokyo/NRT, and Los Angeles/LAX-Tokyo/NRT. Busiest between US and Canada is ORD-YYZ. Busiest between US and Caribbean is MIA-NAS. Busiest between US and Latin America is MIA-CCS. Other busy routes are Miami/San Francisco/Chicago/Washington/Boston/LA-London, Detroit-Amsterdam, New York City-Tokyo, Miami-Sao Paulo, Guam-Tokyo, and quite a few more.
By August 13 there will be a total of 89 flight a day between Chicago (ORD/MDW) and New York (LGA/JFK/EWR).
Here is a breakdown.
American ORD-LGA 20 ORD-EWR 10
United ORD-LGA 17 ORD-EWR 15
Delta ORD-JFK 1 (Comair)
ATA MDW-LGA 7 MDW-EWR 3
Continental ORD-EWR 12 MDW-EWR 4
You'll notice that when it comes to drawing out emptyheaded opinions this topic takes the cake. But if you are interested in flight count (as opposed to passenger count) you can always go to www.oag.com and count them up for yourself.
Over in Southeast Asia - KUL and SIN have a shuttle system jointly operated by SIA and MAS - during the holidays and peak periods in the past there have been 747s and other wide-bodies operating almost every hour. Of course - that's all changed now...
BKK and SIN is another major air corridor with many airlines operating on this sector.
Taipei has two routes that are pretty densely traveled:
to Hong Kong there are 34 weekday flights among China Airlines, Cathay Pacific, and EVA. This number will increase soon because DragonAir recently received approval to serve this route. Most of the flights are widebodies like 747 and A330.
to Kaoshiung there are 60 weekday flights. Three airlines fly hourly services on A321, 757 and MD90 aircraft. Mandarin Airlines, the fourth airline serving this route, has 9 daily flights with F100.
Different people use different methods to determine what "busiest route" means. Some say it's the number of seats offered between the two cities. Some say it's the actual origin-destination traffic. Some others say it's all the traffic on route (including connecting passengers). Still others just count the number of daily flights. And there are those who multiply passenger count by the distance traveled, as in ASMs and RPMs. That's how a long-haul route like New York-London or New York-Los Angeles is considered "busier" than a short Los Angeles-San Francisco route that has more than 100 daily flights.
I think each method of counting is equally valid as well as misleading. I like the passenger count method but since airlines usually don't disclose passenger counts, especially on international routes, I always wonder where people get these numbers or how they estimated them.