He has all the opportunity and gifts to be a hero or one of "the good guys" if you like but because of a tragic flaw, that is arrogance and supreme jealosy for Illuvitar he turns his ways to evil. We, as the audience, feel sorrow and fear for a being so mighty and powerful as him to be so utterly turned to evil.

Although he is not killed, as such we do see his fall and banishment from Arda.

:I would also like to mention Cirdan; I know there is no "proof" for this, but I believe he was one of the elves that woke up by lake Cuivinen. That would be logical, since he was a lord among the elves even in the beginning. The reason for him being a tragic figure, is that he has been witness to and seen all that has come to pass throughout the ages since the first children of Illuvatar awoke. And it is his fate to wait along the shores of Middle-Earth and not depart before the last of the elves leave this world for Aman. I think this is the reason for that he, by the end of the Third age, seems like an old man. He is indeed ancient, and has witnessed and taken part in all the tragic events that formed the history of the elves; all of this must lay heavy on his heart.

I wouldn't describe Cirdan as a tragic character from a strict definition of a tragic character/hero but I understand your point and I do see the tragedy of his life and role in the end.