I've been slightly obsessed with different coffee brewing methods since my wife and I started traveling more and in my opinion you can't beat Turkish/Greek coffee for taste and simplicity. Grind the beans super fine, mix with water in the briki, heat, and pour out into a cup. No filters or moving parts to deal with, and just as easy to do over an electric stove, gas stove, or camp fire.
Just don't drink the stuff at the bottom of the cup ;)