The title of "America's most unloved coin" has a few contenders. The Susan B. Anthony dollar, unused in commerce, with an unattractive design. The twenty-cent piece, resembling a quarter, only minted for a few years. But my nominee is the Trade dollar.
Trade dollars were minted to compete with dollar-sized coins from other countries, an experiment that failed. Many of those that circulated were chopmarked. This is the only U.S. coin that was demonetized; they were available for less than a dollar at one time. These coins will never be number one on the collecting hit parade. Most people don't even realize they exist.
When speaking of "Liberty Seated" coins, most collectors think of the famous Gobrecht design, used for over fifty years. The Trade dollar design is a Seated design. It is not unattractive. And for the numismatist who want something really different--and rare--many pattern Trade dollars were struck.
Trade dollars make a lovely collection. I once saw a set of proof Trade dollars, in a custom-made holder, change hands at a major show. If you stick to mint state, there are varieties and even Carson City issues to keep you looking.
Trade dollars...unwanted, unloved...but worthy of attention.