There's a great section of Ducati.com dedicated to the company's heritage. The site chronicles the history of Ducati products for each decade from the 1920's through the 2000's, and includes a fabulous photo series:
1920s: Ducati was founded in 1928 and initially produced tubes, condensers, and other radio components.
1930s: The company's radio business continued to grow in the 1930s, and would become an important supplier to the Italian military during WWII. Later, the company's factory (pictured here) would be a target for Allied bombing runs.
1940s: As WWII came to a close, Ducati began manufacturing motors and motor parts. It famously introduced the Cucciolo, a motor that could be attached to a bicycle, in 1946. By 1950, Ducati had sold 200,000 Cucciolos.

1950s: In 1952, Ducati released its first complete motorcycle, a small 60cc scooter called the Cruiser. This bike weighed only 98lbs. A few years later, Ducati created the first 100cc racing motorbike, the Marianna (pictured below).
1960s: The 1960s marked the rise of single cylinder racing motorbikes, including this racing bike, an evolution of the first Mach 1 production bike.
1970s: During the 1970s, Ducati developed the 90V Twin, two valve engine. The engine was showcased on popular hypersport production bikes like this 750 GT.
1980s: In 1983, Ducati was purchased by the Cagiva Group and the new management was determined to take Ducati to the top of the new Superbike era. During this period, the company manufactured the now ubiquitous Quattrovalvole water-cooled four-valve engine.
1990s: In 1993 Ducati launched the Monster, a "naked" bike that was stripped of all inessentials and quickly became a design icon. Monster designer Miguel Galluzzi said of the philosophy behind his
creation: “All you need is a saddle, tank, engine, two wheels, and
handlebars.”

2000s: The SportClassic family represents the union of between the fascinating style of the 1970s and Ducati's advanced technology of today.
[Photo credit: Ducati.com]