The Godfather (1972)
The plot of the first movie begins in 1945 with Michael Corleone (Al Pacino), the youngest son of the Don of the Family, Vito Corleone (Marlon Brando), returning from World War II and reuniting with his family at his sister Connie's wedding. The good times don't last long, however: shortly after the wedding a captain from a rival crime family tries to interest the Don and his Hot-Blooded eldest son, Sonny (James Caan), in the new up and coming moneymaker: heroin. The old fashioned Don is not interested, believing that selling drugs would wreck the political connections vital to the family, but when Sonny shows interest the rival family decides on a new course of action: kill Don Vito, and try to make a bargain with Sonny afterwards.
The assassination attempt on the Don fails to kill him but puts him in the hospital and Michael, who has never been interested or involved in the Family business before, thwarts a second attempt while visiting his father at the hospital. At a truce meeting Michael kills both the captain from the other family and a police captain that was involved in the second attempt at his father before going into hiding, and Sonny, furious at the attempts at his father's life, declares an all out Mob War.
Eventually Sonny is ambushed and killed, and Michael is forced out of hiding to try to take over the family. Michael pretends to be helpless at first, but after his father dies and he becomes the head of the Family, Michael ruthlessly purges The Moles within the family and his enemies in the other major mob families, leaving the Corleone family as the most powerful force in the mob scene.
The Godfather Part II (1974)
The second film continues Michael's story around 1958 while giving flashback accounts of the young Don Vito (Robert De Niro) from his troubled childhood to his eventual turn to crime and rise to power (based on parts of the original book which were omitted from the first film). In the present Michael is juggling many problems, which include he and Jewish gangster Hyman Roth trading double-crosses and assassination attempts even as they do business together, his personal life with his wife and family crumbling, and the Corleone family trying to survive an investigation from the US government.
Eventually Michael manages to overcome everything, but the film ends on a theme of Pyrrhic Villainy: Michael's actions have destroyed his family, ended his marriage, he's killed his sole remaining brother, Fredo, after finding out that Fredo made a deal with Hyman Roth, and ends the movie utterly alone.
The Godfather Part III (1990)
Many fans prefer to disregard the third film entirely, which is completely original and picks up events 20 years later in the timeline. Here an ailing and guilt stricken Michael increasingly attempts to make the Corleone family legitimate, but in doing so becomes less and less involved with the functions of the crime family, which gives more leeway to unscrupulous and unprincipled associates. Sonny's bastard son Vincent, a member of the crime family, speaks up about this and is taken under Michael's wing and groomed to replace him. There is one last round of assassinations and purges in the Corleone Family before Vincent becomes the new Don and, years later, Michael dies.