Longbow: Bamboo, Yew, Canarywood, Zebrawood, Red Elm, Black Walnut, Cedar, Cherry and Maple

Recurve: add Osage, Black Locust, Bocate to the above list.
These last woods can be used in longbows as well but I prefer to use them as veneers over one of the woods listed in the longbow list.

Almost any wood will work if it is ground into a thin veneer.

May you be forever blessed with favorable winds and clear trails.