1991 Trek 930, 2005 Bianchi Eros, 2006 Nashbar "X," IRO Rob Roy
if you're referring to bikes like the Electra Townie, etc.: it lets you have complete leg extension (better pedaling efficiency), but place your feet down flat footed without standing at stops (more comfort).
It seems to play on the idea that lying down is more comfortable than being upright. Leg extension without one's weight over the pedals makes it difficult to develop power or deal with bumps. The neck position can be just as uncomfortable in reverse as cranking the head up off drops is. It can be hard to do a shoulder check. Like anything else it is a mater of trying it out, if your LBS has something for you to try, and seeing how you like it.