The advantages of a wood-burning stove are obvious. The fuel is free. It's readily available just about anywhere you hike. You save money and weight every time you backpack. Plus you need relatively little wood—just a small collection of twigs, really—to boil water or cook food, minimizing your impact on the land. And a range of lightweight and proven wood-burning stove designs are available—I've highlighted three of the most popular below.
But with these advantages come some significant drawbacks. The stove and pots—plus anything they touch in your pack—become blackened and sooty. You'll spend time (and must have the skills) to find sufficiently dry fuel and get a fire going, even in damp, wet, or windy conditions. And wood collection may be banned (or severely frowned upon) where you're headed, especially in high-use areas.
This is the leader of the wood-burning pack, with an excellent and compelling website to match.
Per the product description, "the Solo Stove is a natural convection inverted downgas gasifer stove." What this teched-out description (gasifer?) means, it seems, is that the stove features two points—at the bottom and top of the burn chamber—where oxygen enters to help ensure a more complete combustion with minimal smoke. (Here's a nifty diagram that shows it in action.) Made of built-to-last stainless steel, it weighs 9 ounces and retails for $69.99.
Sierra Zip Stove
This stove's distinguishing feature is a small battery-powered fan that feeds oxygen into the fire and whips the flames into a cooking tornado.
As campy looking as it is effective, the Zip Stove has been around for many years. What's new, however, is a titanium version ($129) that weighs in at a much lighter 10 ounces compared to its stainless steel forbear ($57).
Emberlit FireAnt Multifuel Stove
Relatively new to the wood-burning space is this titanium featherweight, which weighs in at a mere 2.8 ounces. The simple design collapses down for easy storage and is also compatible with Trangia and Esbit burners and solid fuel tabs. $69.99.