Traditionally, tragic heroes may possess many admirable qualities, but among them is one tragic flaw that puts them at odds with their destiny, their companions, or the powers that be. Ultimately, it leads to their destruction.
Most often, this tragic flaw is the hero's pride or arrogance - the hero's hubris. Tragic heroes are nearly superhuman, but they have a big ego. They ignore warnings or defy the moral code, thinking they are above the laws of gods and men. This arrogance brings the wrath of retribution upon the hero, and he dies inadvertently by his own hand.
Hubris is not the only tragic flaw. A hero's tragic flaw could be as admirable as a paladin's unwavering devotion to his patron god. He dies fighting in the name of everything good, but he still dies because of it. Another tragic flaw could be the inability to have faith in one's self, and at the moment the hero needs to overcome his doubt, he hesitates, and the enemy strikes him down.
The common misconception about tragic flaws is that only tragic heroes can have them. If a character has a tragic flaw, then he must die, right? I don't think so.
If you remember the Hero's Journey model, the Ordeal and the Resurrection are both considered life-and-death moments. Now consider for a moment that your hero has come to the brink of destruction due to his tragic flaw. The tension suggests that the hero is going to die. All tragic heroes die. But the reader forgets, this is no tragic hero.
The hero faces the Shadow at the Ordeal, and perhaps he fails. His tragic flaw prevents him from conquering the enemy. He comes close to death, and it seems that there is no hope in him succeeding his quest. He struggles and fights for his life, doubting himself and having little optimism for what is to come. He comes to the Resurrection stage of the journey and faces his enemy again. But this time, he's learned. He realizes his tragic flaw and overcomes it. He defeats the enemy, triumphing over both the dark forces that oppose him and the dark forces within himself.
By definition, he isn't a tragic hero. He didn't die. But he did. His old self died; the part of him that harbored that tragic flaw for so long died. The hero has been born anew.
Every well-rounded hero has a trace of this tragic flaw, some weakness or fault that makes him thoroughly human and real. Perfect, flawless heroes aren't very interesting. They're difficult to relate to.
Archetypes, stereotypes, and common plot devices are known to both reader and writer. As the writer, we can use the familiarity to trick the reader, luring them into a false sense of security, and then we pull the rug from under their feet, turning all they thought they knew on its head. As with the tragic hero, we know he is going to die, but if he earns his way out of physical death and transcends a metaphorical one, the change is welcomed. Think of other traditional dramatic concepts that can work for the heroes in your story. By employing these ideas and structures, you can create a familiarity for the reader, and by changing them slightly, you can surprise your audience (in a good, not-contrived way) and offer the pleasure of catharsis.