Heck, REI has a whole array of camping/hiking coffee makers and accessories–including hand-cranked grinders if you’ll be going for more than a couple days. I have a 4-cup Lexan French press, and it works great. Just swish it out with a little water after making the coffee, and wash it when I get home.
For the past 20 years we’ve used a 10-cup percolator on a propane stove. Has a filter basket that takes little tiny circular filters, and makes great coffee. Plus you get the entertainment value of watching the coffee bubble up into the little glass knob; and use its color as your determination of done-ness.
My friend just bought a drip coffee cylinder doohickie. It’s got a superfine stainless steel mesh at the bottom so it’s easily cleaned and doesn’t require a paper filter. It somehow sits on a mug. I think it’d work well for backpacking.