What role in what film was turned down by the most actors?

 The role of Neo was offered or “floated” to the following actors who all showed no interest or decided to pass:

Keanu Reeves as Neo in The Matrix. Source: Looper

• ​Will Smith
• ​Brad Pitt
• ​Leonardo DiCaprio
• ​Nicolas Cage
• ​Val Kilmer

​They finally went with Keanu Reeves, who had recently starred in a string of box-office flops and wasn't viewed as the surefire blockbuster anchor the studio desperately wanted at the time.

​Oddly enough, the studio was so eager to land a bankable A-list star that they pitched it to Sandra Bullock. They told her that if she accepted the part, the writers would completely rewrite the script to make Neo a female character. She turned it down.

​A number of the actors listed would have made for very interesting takes on the film—Will Smith’s trademark charisma, for instance, would have drastically changed the tone. But Keanu still made it work. Good movie!