Oh, Aero42, you will have to be much more specific for having any numerical values on this subject.
First the 737 has been built in nine different major configurations named 737-100 up to 737-900 (the 900 not in service yet).
Some of the nine types have been made for various maximum weights. Obviously those with a lighter max weight don't need to be as strong here and there, and are consequently built lighter, and visa versa.
Most of the types have come with slightly different engine subtypes, some optimised for economy, some for hot&high performance.
The actual load (payload + fuel load) means a lot to fuel consumption.
The altitude, at which you fly, also means a lot. Most often the flight crew don't decide that, ATC controlers do.
Often, because of other traffic, you have to change altitude several times during a flight, it costs fuel.
Different airlines equip their planes with different interior of different weight.
Some airports restrict climbout to minimise noise. Often it means more fuel consumption because flaps must be extended for a longer time.
Are you allowed a straight in landing, or does ATC put you on hold and tell you to descend one flight level at a time, and do it as fast as possible making room for the one above you.
At what speed do you fly? In calm weather there is an optimum speed. There are other optimum speeds for any amount of headwind or tailwind.
Have you had enough? Or should I also mention air temperature and humidity? Small factors, but noticeable.
Of course the fuel consumption at level flight also goes down all way during the flight simply because the plane get lighter as more and more fuel has been burned.
You can have thousands of answers to your question.
How much fuel will be needed for a flight, that is something the flight crew calculates according to all these variables before every flight even if they have flown the same sector a hundred times before. And after the landing they sometimes are surprised about how wrong they calculated.
But whatever calculations you may do, then you should come out with the result that the 737-600 is probably the most economic airliner considering fuel burn per hour, while the similar sized 737-200 is a real fuel guzzler.
Did it help? At least it didn't answer your question.
But anyway, let me give you an answer: 1000 - 2000 US gallons/hour depending on circumstances.
Best regards, Preben Norholm
Always keep your number of landings equal to your number of take-offs