Since I've never heard of an instance, this question would apply to all of human history and all regions.
Today, in the modern industrial world, arrow shafts made of aluminium alloys, fibreglass reinforced plastic, and carbon fibre reinforced plastic are very common. These shafts are usually hollow tubes of these materials, but there are some exceptions (e.g., very thin solid carbon fibre shafts for low drag, heavy solid fibreglass shafts for bowfishing).
Before those materials became available, the usual materials were wood, bamboo, and reeds. Bamboo shafts could either be made from whole thin canes of bamboo, or could be made by splitting the walls of larger bamboo. In a scientific technical sense, bamboo and reeds are not wood, but bamboo is often considered "wood" in everyday English usage. Wood and bamboo are still commonly used together, and are often preferred over modern materials by "traditional" archers.
While these were the usual materials, there were some exceptions. In some Arctic regions, where wood could be very scarce, some arrow shafts were made of bone (usually multiple pieces joined together). Some Chinese arrowheads had very long tangs - in ancient China, these often had iron tangs with bronze heads cast onto the tang, and during the Ming Dynasty, they were usually all-iron. The tangs of these were as long as the shaft, which was usually bamboo. The effect was to produce an iron-cored bamboo shaft. Arrows constructed in this way were called "iron arrows" in Ming China. This construction was usually used for crossbow bolts rather than for arrows to be shot from a hand-bow, but the archery component of the Korean military examinations included shooting an "iron arrow", which was possibly the same type of construction. These were shot using a high draw weight hand-bow. The heaviest type of Korean military examination iron arrow weighed 240g, and might have used a solid iron shaft (about 6mm thick) rather than an iron-cored bamboo shaft, but the lighter types (160g and 60-64g) probably used composite iron-cored shafts.
Arrow shafts were often made in two pieces, with a foreshaft usually made of a different material fitted to the front of the shaft proper. While shafts were usually wood, bamboo, or reed, the foreshafts were made of a wider variety of materials, including bone and ivory (the most common materials were wood, often hardwoods denser than the shaft proper). An example of reed arrows with bone foreshafts:
Wood and bamboo arrow shafts might also be bound with silk thread or sinew, to produce a composite shaft.