Known to many as the Lion of Jesi, he was born in Filottrano and then he moved to Iesi with his family. Falappa began his racing career in motocross before making the switch to road racing in 1988. In 1989 he moved up to the Superbike World Championship riding for Bimota, winning 3 races and finishing the season in sixth place. Falappa moved to the Ducati team in 1990. His best result was a 4th place finish in the 1992 season and a 5th place in the 1993 season (winning 7 races, including the season's first 3).
In 1994, Falappa crashed while testing a factory Ducati 916 and suffered serious head injuries. After being in a lengthy coma, he eventually recovered, but never raced again. He won a total of 16 races in his Superbike World Championship career.