Creasy: Okay, my friend. It's off to the next life for you. I guarantee you, you won't be lonely.
Rayburn: A bullet always tells the truth.
Fuentes: A last wish, please, please. Please.
Creasy: Last wish? I wish you had more time.
Creasy: Forgiveness is between them and God. It's my job to arrange the meeting.
Rayburn: A man can be an artist... In anything, food, whatever. It depends on how good he is at it. Creasey's art is death. He's about to paint his masterpiece.
Samuel: So what happened?
Jordan: Family paid the ransom. And they sent the kid home after a couple of days... Minus an ear, of course.
Answer: Creasy was a contract assassin for the CIA. His downfall was his drinking because it affected his reaction time and so forth. He had a lot of bad memories he was trying to live with. He considered this bodyguard assignment to be a blow off assignment. This and his bad memories combined with his drinking problem, made him severely depressed. This is why he considered killing himself. At the end of the movie, you see Creasy being taken away in a car. His gunshot wound from the "Voice's" brother, along with his prior gunshot wounds that were never properly treated, had finally gotten the best of him. He was bleeding the whole last half of the movie because he never fully recovered from the gunshot wounds. So, to answer the question of why he died, he bled to death.