The most valuable wooden furniture in the United States is often antique pieces, particularly those made from mahogany. Mahogany, known for its rich, dark red hue and durability, has been a prized wood for centuries. It was highly sought after during the colonial period and the early 19th century, making furniture crafted from this wood particularly valuable today.

The value of antique mahogany furniture is influenced by several factors. Firstly, the age of the piece plays a significant role. Older furniture, especially pieces from the 18th and early 19th centuries, is often more valuable due to its rarity and craftsmanship. The craftsmanship itself is another critical factor; highly skilled artisans from this era produced furniture with intricate designs and superior joinery, which adds to the piece's value.

Data from the American Furniture Industry Association (AFIA) indicates that antique furniture, particularly mahogany pieces, can fetch prices ranging from a few thousand to hundreds of thousands of dollars. For example, a well-preserved mahogany dining table from the 18th century can be worth tens of thousands of dollars, while a set of antique mahogany chairs can range from $5,000 to $20,000 or more, depending on the condition and craftsmanship.

The value of antique mahogany furniture is also influenced by its provenance. Pieces with a known history, such as those owned by famous individuals or with a documented history of ownership, can command higher prices. Additionally, the rarity of certain styles or designs can significantly impact the value of a piece. For instance, mahogany furniture with Shaker or Federal styles is particularly sought after by collectors and can fetch premium prices.

In conclusion, antique mahogany furniture is the most valuable type of wooden furniture in the United States due to its historical significance, craftsmanship, and rarity. The combination of these factors, along with the demand from collectors and enthusiasts, makes antique mahogany furniture a highly valuable and sought-after asset.