Creon shows up in all three of Sophocles' Theban plays. He goes through quite a transformation over the course of the story. In Oedipus the King, he seems like a totally rational guy. His cool reason highlights Oedipus's hot temper. In Oedipus at Colonus he becomes the full-fledged smooth-talker he had in him all along. He attempts to sugarcoat his plea for Oedipus to return to Thebes, and could be seen as cowardly and weak when he kidnaps Oedipus’s daughters.
By the time Antigone rolls around, Creon, the play's antagonist, has become an absolute tyrant. His hyper-logical mind refuses to recognize the bonds of familial love that tie Antigone to her brother Polyneices. He rejects the irrational laws of the gods in favor the rational laws of man. It's interesting that the cool reason that seemed like such a good thing in Oedipus the King now causes his downfall. Hmm, we detect the distinct scent of Sophocles' favorite dish: tragic irony.
One of the things that sets great tragedy apart from mere melodrama is that all the characters ultimately have good intentions. The plays become tragically ironic when these good intentions bring misery and horror for all. Though, it's easy to pigeon-hole Creon as a big mean man, persecuting his brave, innocent niece, it's just not that simple. In great tragedy, there are antagonists (like Creon) but there are rarely villains.
The first thing Creon does in Antigone is declare a harsh but understandable law. He proclaims that while the body of Eteocles will be buried with dignity, the corpse of Polyneices will be left to rot on the field of battle. Anyone who attempts to honor Polyneices's body with burial will be sentenced to death. Sure, it's not the nicest law, but think about this: Polyneices is a traitor. He allied with other city-states and attacked his hometown. He nearly brought on the whole sale destruction of Thebes.
Of course, Polyneices only led this attack because his brother Eteocles refused to share the throne as they had agreed. Still, many Thebans have lost fathers, brothers, and sons, because of Polyneices's assault. In the parados the Chorus expresses anger at Polyneices and joy over his defeat, showing that the people of Thebes are none too pleased with his actions. The people, represented by the Chorus, seem to support Creon's decree.
Here's a hypothetical, similar to the one we pose in Antigone's "Character Analysis": what would happen today if one of America's top generals allied himself with terrorists and led an attack on the U.S.? If such a person died in the battle would they be buried with full honors in Arlington? The president would have a really hard time justifying such an action. Sure the body would be allowed burial somewhere, but still (just as in ancient Thebes) the traitorous soldier's remains would most likely be in some way symbolically dishonored.
Though Creon's first law as king isn't totally unreasonable, it does turn out to be a really, REALLY bad idea. Creon makes matters worse by refusing to relent in the face of mounting opposition. His tenacious allegiance to the laws of state turns out to be his hamartia, a word commonly referred to as tragic flaw, but more accurately translated as tragic error.
It's interesting that we see him behaving much the way Oedipus does in Oedipus the King. Ironically, Creon starts accusing everybody of conspiracy, just the way Oedipus accused him. Also like Oedipus, he disbelieves the words of the blind prophet Teiresias. When the seer predicts that Creon's course of action will result in the death of Creon's whole family, the paranoid king accuses the seer of having been bribed.
Once again, though, what seems to be a flaw is also in some ways a virtue. Creon's fierce dedication to law and order seems to be exactly what Thebes needs. The city is just coming back together from a state of total anarchy. The people need a strong and steadfast leader to bring them together. How's it going to look if Creon goes against the very first law he makes? Creon's concern for his public image is certainly in some ways self-motivated. He doesn't want to get punked down, especially by a woman. However, this seemingly selfish worry also comes out of a concern for his people. A wishy-washy leader can be a very dangerous thing in a time of crisis. If Creon appears to be weak the whole city could descend back into chaos.
Also notice that Creon isn't totally dogmatic about his decree. Slowly, over the course of the play he becomes less and less extreme. First he relents on having Ismene executed along with her sister. Next he has Antigone entombed instead of outright executed. In the end, he is ultimately convinced by Teiresias's prediction and goes to release Antigone. Unfortunately, he's a little too late. Before he can stop it, his niece, his son, and his wife have all committed suicide. At the play's conclusion, Creon's downfall becomes symbolic of the tragedies that occur when the laws of man attempt to compete with the ancient laws of the gods.
For more Creon check out Oedipus the King and Oedipus at Colonus.