There is a famous example:
Tom Selleck (Indiana Jones): Selleck declined because of his commitments to Magnum PI. The part went to Harrison Ford.
A more recent one:
Ben Affleck (Brokeback Mountain): One of the actors whom director Ang Lee talked to about starring in the love story between two ranch-hands. The part went to Heath Ledger.
And two that get the head spinning:
Kevin Costner (The Matrix): Costner was apparently considered for the role of Neo (seriously). The part went to Keanu Reeves.
Chevy Chase (American Beauty):Turned down the lead role of Lester. Jeff Daniels was also considered for it. The part went to Kevin Spacey.