Courier companies routinely book one seat each way, every day on flights between two major business centers. For example, from New York to Hong Kong. These are always economy class, generally on major airlines, and usually a flight that departs in the evening. Of course, the airlines give them a very good price.
You can occupy that seat at a discount -- provided you take their stuff. A company representative will meet you at the airport with your ticket, the shipment (which is checked in for you) and the shipping documents (which you carry), and another will meet you at the other end to take delivery. You just deliver the documents, and they do the rest. In no case, do you have to help with carrying their luggage load.
Sometimes, someone will also meet you in the middle; e.g. on a Sydney-London courier flight, you stop in Tokyo, where you drop off the Sydney-Tokyo stuff and pick up Tokyo-London.
Discounts are often substantial, 20% and up. Once the company knows you as a regular and reliable courier, deals may get even better. If someone cancels and they are stuck, they may offer a last-minute free flight. In other words, someone else paid dearly for your free trip!
A few years back, courier travel was possible within North America or Europe. That has been eliminated by air express companies such as FedEx and DHL which have their own planes or long-term contracts with the airlines. Nowadays, courier flights are almost all intercontinental.
Courier travel is not for everyone, and there are serious restrictions:
If you cannot live with these restrictions, see the Discount airlines or Airline consolidators articles. Fares will likely be a little higher, but there is more flexibility.
Below are two major companies which can arrange courier flights. Both charge a fee for membership, and offer other discount travel options as well.
Booking through an agency is generally worth the small fee of joining the agency, as they are given most access to the flights. They may be able to offer flights that you could not find as a freelance courier.
You need to be very careful about the legitimacy of the jobs you take. The last thing you want is to be caught transporting contraband (or worse) on a plane. A good way to avoid this is to use an agent (usually a representative of the service you are working for), who will take you through customs and clear the contents. Always check the repuation of the courier company before booking. None which are reliable and legitimate would ever try to ship anything illegal.