With the exception of olive trees and grape vines, all species of wood is deemed by the sages as kosher, fitting to be used for the altar fires (Midot 2,3). These two were disallowed for two reasons: because they do not burn well, and emit large amounts of smoke; and also, because they are both important for the habitation of the Land of Israel - a primary concern for the sages. Since these two trees both give forth fruit that is essential to sustenance of the nation, they are given special status.
While it is permitted to use any other wood for the altar, it was customary to stock the arrangements with the branches of three particular types of wood: fig, walnut, and pine. These woods all burn well, and were therefore preferable for the altar.