One of the most popular recreational aircraft of all time qualifies as a light-sport aircraft: the Piper J-3 Cub. Designed in the 1930s, the Piper Cub is no longer in direct production, but you still can get a modern version known as the Taylorcraft F-19.
The Piper Cub is a two-place (tandem), high-wing, fabric-covered taildragger built from 1938 to 1947. Its offspring, the Super Cub (not sport-pilot eligible) was produced into the 1980s. If you're not in a hurry, the Cub is your friend as it cruises at about 75 mph, depending on whether it has the Continental 40 or 65 hp engine. For the record, there are more than 40 older Piper models that technically qualify as eligible for sport pilots.
By today's standards, the Cub is a very slow aircraft. However, if you're not in a hurry and you're looking for nostalgia, the Cub is a great airplane for sport pilots.