Ajax features Ajax as a man who is determined to follow his will, no matter what, without the help of the gods. This is very dangerous.
Oedipus' determined thirst for knowledge, even when the truth is utterly horrible, is his most important character trait. Even when he blinds himself and is forced to live as a beggar, he still operates by sheer force of will in both Oedipus Rex and Oedipus at Colonus.
In Electra, the main character will not give up mourning her father until he's avenged, will not act like a woman and accept her place, and will not submit to her stepfather Aegisthus' and Clytemnestra's abuse. When she loses all hope of salvation (thinking Orestes is dead) and has been told of her parents plans to seal her in a cave to die, she decides to try and kill Aegisthus herself, in spite of being a woman.
Sweeney Todd, in his Sondheim incarnation. Survives fifteen years in a penal colony, escapes, flees to the coast, builds himself a fucking raft and tries to sail to London from Australia. Of course, he gets picked up by Anthony and the good ship Bountiful en route, but still...
Just to underline the above: Oscar Wilde was sentenced to two years' hard labour, and was told that he'd be lucky if he survived eighteen months. Sweeney must have been a terminator in human form to survive fifteen years, and have enough strength to escape successfully.
In Man of La Mancha, Don Quixote's Determinator frame of mind is expressed in "The Impossible Dream":
This is my quest, to follow that star No matter how hopeless, no matter how far To fight for the right, without question or pause To be willing to march into Hell, for a Heavenly cause... And the world will be better for this: That one man, scorned and covered with scars, Still strove, with his last ounce of courage, To reach the unreachable star.
John Adams in 1776. At the start of the play, he's proposed independence twenty-three times despite the fact that it's always shut down even before debate. He wavers after the Southern walkout, but Abby's reminder of his beliefs and her timely gift of saltpeter gets him back downstairs and badgering his stricken colleagues to whip some votes. And the Eleven O'Clock Number number he sings right after has him reaffirming that he will not give up on independence.
For I have crossed the Rubicon Let the bridge be burn'd behind me! Come what may, come what may... COMMITMENT!