Chairs can be built from any wood available. For fine furniture, the hardwoods are the best choice, but some of the most comfortable chairs are built from some of the softest woods. Some of the hardwood chairs take special blades, while most of the softer woods can be used with any tools available to the handyman. If your are going to build a mission-style chair, use hardwood. For an Adirondack-style chair, go with soft.
For traditional strength and longevity, no other wood lasts like oak. It has a tight grain pattern that is somewhat chaotic. This means that it is unlikely to split down the grain pattern. It's not prone to shrinking as much as other semi-hard woods, and has that familiar look of fine furniture. There are two species of oak used in chair making--red oak and white oak, with white oak being the hardest and tightest grained. These hardness characteristics can also mean that it is harder to work with.
The availability of mahogany worldwide makes it an obvious choice for making chairs. Its warm colors and semi-soft texture make it easy to work with. It is straight grained, blends well and is reasonably stable due to straight-grain patterns that are usually laminated, making a mahogany chair almost split proof. Mahogany grows on every continent, therefore, there are probably more mahogany chairs in the world than any other specific wood.
Maple has an extremely tight grain pattern that is also chaotic like oak. On a hardness scale maple is the hardest wood available, second only to birch, which is rarely used for furniture. Maple has a warm, light-colored glow that makes it great for chairs, but only the sharpest, carbide-tip saws and drill bits are recommended for milling maple. Glue will sometimes fail to adhere to the smooth, hard surface on the inside of dowel holes. Care and patience need to be applied when building a chair out of maple.
Poplar has also become a widely used wood for chair making because of its flexibility. You will see poplar in bent wood chairs. The chair part components like bent legs and backs are glued up from thinly sliced veneers that are compressed and formed into curves. The craftsman fashions chairs out of these bent parts, since unusual designs can be fashioned with bent wood. These chairs are also very comfortable, as poplar has some flex to it. Unfortunately, this flex factor can also lead to the chair lamination separating if abused.
Cedar and Redwood
Two of the oldest woods in use are the most traditional as well. The famous Adirondack-style chair has been around since before the Civil War. These are the only two woods that are suitable for outside use, as they won't deteriorate or rot. They are soft, easy to work with, and very comfortable because of a slight flex. Generally not used for fine furniture, redwood and cedar are almost exclusively used in picnic, deck and lawn chairs.