The best place to buy cheap international plane tickets is online. We've tried travel agencies and they can't compete with the discount ticket websites. You can search google ("cheap airfare South America", for example), or go straight to one of the well-known sites, like Expedia, Travelocity, Cheap Tickets, Hotwire or Priceline.
I just did a quick search for the cheapest airfare from Tucson, Arizona, to Buenos Aires, Argentina, using the five sites mentioned. They ranged from $1221 down to $873, and there were fares as high as $3728. Hotwire happened to have the cheapest, but they were the worst of the five when I searched for a domestic flight earlier. You cannot say which service will find the cheapest international plane tickets from week to week. My number one money-saving tip is to always check several websites when shopping for inexpensive flights.
My Accidental $1000 Discovery Before going to Ecuador, I searched several websites that deal in cheap international plane tickets. The cheapest airfare from Traverse City, Michigan to Quito, was $1720. Out of curiosity, I checked Miami to Quito, and it was only $400. Airfare from Traverse City to Miami was $300. Book two separate flights and save more than $1000! The discount sites aren't set up to check in this way (yet), so you have to do this on your own.
If your first flight is late and you miss the second, you may not get a refund, but it is still cheaper (every time I checked) to just book a flight to Miami and catch a flight to Quito without a reservation, thus avoiding this problem. This strategy is best for those in towns without international airports. If you live in Miami, you already have cheap international airfare.
Courier Flights As an air courier, you can get really cheap international plane tickets. Courier companies ship material in the luggage space of an aircraft passenger because it can be quicker, cheaper, and more reliable than sending the shipment unaccompanied, since checked luggage bypasses many of the typical customs delays. The courier company begins by purchasing airfare, and then they resell the plane tickets to you. In exchange for your luggage space, they give you a discount on the airfare.