I ask this question pretty frequently, and get lots and lots of smart answers, but none that really satisfy.
What is the definition of protagonist?
Can we come up with a simple, concise definition? Every time I try, I come up with reasons that the definition fails.
If we define the protagonist as "the character we root for," then this presumes that the protagonist's goals are always worthy. In the case of tragedies, they frequently are not. Really, did anyone actually want Oedipus to marry Jocasta?
If we define the protagonist as "the character in active pursuit of a goal," then this eliminates an entire class of protagonists whose only true goal is to preserve the status quo. Think of thrillers. Think of a bodyguard hero. His goal? To have nothing change. The antagonist -- the bad guy with an ax to grind and bullets to spare -- is the one who sets the plot in motion by setting a goal of killing the bodyguard's protectee.
If we define the protagonist as "the character on the stage or on the page most frequently," then ancient pieces with narrators and choruses get a bit muddled.
If we define the protagonist as "the character with the most central role in the plot," then what on earth do we do with ensemble pieces? Really, who was the protagonist in Crash? In The Big Chill?
And then there's romance. Can a story ever really have two protagonists?
I'm throwing this out there as food for thought and because I'd like to hear what everyone thinks. We've got some smart people hanging around this little blog.