There are some insanely-cheap flights around now, mainly flying from the US to Africa in January and February 2015 with Delta Air Lines, with some to Western Asian countries like Oman. It seems a bit hit and miss but some flyers have reported successes, so it's certainly worth a try.
Flyforfree published a cheap flight from New York to Dar es Salaam, Tanzania ($467 RT), but I searched several dates in January and February on Seat24 and Wideroe and couldn't find any at that price. Try your own dates and cross your fingers!
Then FlyerTalkers found various destinations from the US to East Africa, and noticed that the cheap flights are also from LAX, ORD, IAD and BOS.
I tried searches such as Los Angeles to Nairobi, New York to Entebbe, Uganda and New York to Nairobi (booked by a FlyerTalker for $335 RT) and I couldn't find any flights that cheap.
I did, however, find these two gems that both work out at just 2 cents per mile:
Washington to Nairobi $310 RT – Book on Seat24.
Washington to Muscat $348 RT – Book on Seat24.
Some FlyerTalkers have been unable to process an order with their credit cards; others have been successful. Some have reported the price increasing at the credit card stage. Some have booked successfully and then received a cancellation email.
Good luck with your searches! Let us know if you manage to bag a cheap flight.