Even your 737 and A320 can carry a good amount of cargo. It may not be in the form of containers as it is with the widebodies, but I have watched large amounts of cargo loaded onto aircraft such the 737 and A320, especially on shorter haul international flights, i.e. Canada, Mexico, Latin America & Carribean Islands. I've seen them take pallets of large boxes out by the plane and start loading box after box. The planes might be narrow-body aircraft, but they can certainly haul a decent amount of cargo in addition to passengers & their luggage.
When it comes to other flights, especially widebody international flights, in some cases the cargo being carried makes more revenue than the passenger load (as another poster has pointed out). Some international carriers also operate "Combi" aircraft where the front of the main cabin is for passengers and the back of the aircraft is for cargo. I've flown on KL & QF 747 combi's myself, but I also understand other aircraft such as the 737 have a combi configuration.
I'm not sure what airport you work at, TSASCRNR, but you mentioned it is a large international airport; If that is the case, you'd probably be amazed at the amount of freight/cargo that is carried on passenger aircraft -- everything from turbo-props (Dash-8, EMB-120, ATRs), to RJ's (ERJ/CRJ/ARJ), narrow-body aircraft (737/757/A320), to your widebody aircraft (DC-10/MD-11, 747/767/777 and your A300/A310/A330/A340's).
As has been mentioned, US Mail also travels in the belly of commercial aircraft -- however, it is my understanding there is a size/weight limitation with respect to what US mail can be transported. This was done out of security concern as there is no screening of US mail put on passenger aircraft.
From what I understand, air carriers have been lobbying for US Mail screening so larger US mail items & parcels can be transported by commercial aircraft; this in turn would increase revenue for the carriers by allowing them to transport the larger mail items. Anyone know what the latest is on this?
Last but not least, even items sent via one of the popular "next day air" companies will even fly as cargo on commercial aircraft. While these carriers have their own airlines and fleets, there are parts of the globe (and even United States) where use of passenger commercial aircraft is necessary to deliver the packages. I know one of the companies in particular does this, but it wouldn't surprise me if most of them do in some capacity, be it DHL, FexEx, Airborne, or UPS. (note: one of these four is the company that transported the package I refer to in a previous post that was sent to me in the Pacific Northwest. The package not only flew on commercial airliner but was transported via the largest Pacific NW airport; I am not going to name the airline, but it was most definately cargo they transported on behalf of a cargo carrier).
Best,
SDF_Traveler
P.S. I recently did a 6 1/2 hr trans-Atlantic flight on a 757-200, a narrow-body; from my view at the gate, cargo was loaded onto this aircraft. Now, only if the cargo was screened.