Bill Murray is one of the greatest actors alive -- a guy who built his career on comedic roles with an edge, and who has been killing it in his later years with meatier, more dramatic roles in Wes Anderson's films and stuff like 'Broken Flowers.' But back in the late 80s, when Murray was still just a comedic actor, he had the chance to star as Batman in Tim Burton's vision of the caped crusader.
Burton chose Michael Keaton, another comedic actor and former stand-up, to play the part instead, showing audiences that Keaton was capable of something darker than what audiences were used to with him. The result might have been the same for Murray, and if he had taken the part, it might have gotten him into dramatic work a little earlier.
Then again, we really can't picture Bill Murray as Batman -- Batman is cool and all, but Bill Murray is cooler.