Airfare is one of the most cost prohibitive elements of long distance travel. Many people find themselves in situations where they know someone they could stay with in another city - so accommodations would be free - but there's simply no way of being able to get there affordably. In terms of discount travel, there are some solutions to expensive airfares that are worth looking into if you are flexible and interested on a short visit rather than a long trip.
One of the cheapest ways you can fly is called courier flying. How this works is: courier companies exist that specialize in delivering relatively small packages quickly - things like important business documents etc… and what these companies want is your baggage allotment on a flight. So they will offer extremely discounted fares in order to get your baggage allotment.
If you sign up for a courier flight, your job will be to show up at the airport with carry on luggage only, meet someone with a package who will check it onto the plane in your space (you won't normally have to handle the package), and take the flight. In most cases you are required to take a return flight as well in a relatively short time (usually a few days, and rarely more than a month), which is why courier travel is more suitable to quick cross-country visits than long term travel.
Here are some samples of the approximate discounts on return fares, obtained through a simple internet search: New York to Paris, $250; Los Angeles to Sydney, $400. In some cases, if you are on their call list, the courier may become desperate with a last minute flight and offer it for free.
Now, with such extreme discounts, there must be a catch, right? Of course: courier flying would be simply too good to be true it didn't come with an extreme lack of flexibility. Courier flying works by placing yourself on a list to be contacted by the companies. You're not likely to receive much notice, and until you board the plane, your fate is entirely in the hands of the courier company: if there is a change or a problem with the package, for example, you're out of luck.
More so than other types of discount travel, courier flying is dependant on you being able to establish a repoire with the company. If you have been flexible and completed flights for a company in the past, you may be able to establish a relationship where they call you first to offer a flight, in which case you'll have some more options.
Regardless, to engage in courier flying you have to be very flexible, and although it is one of the most extreme forms of discount travel available, it remains fairly restrictive. If you're interested your best bet is to try one or two courier flights and hope that you can establish a good relationship with the company.