Euripides' Medea tells of the trials and tribulations Medea faces through supporting Jason, taking care of her family, and finding solace in her revenge. One could support Medea's actions in two very distinct ways. First, Medea believes that love can make people do crazy things. Second, revenge is one of the strongest motives for action.
In regards to love, Medea commits many murders (her brother and Pelias). She finds that for her to get to and be where she needs to, she must do certain things. Once her marriage to Jason falls apart, Medea realizes that revenge proves to be a far stronger emotion than love. Medea shuns all others, even her own children, to find full revenge.
Therefore, one could argue that Medea's actions are justified by her emotions. Emotions are a very difficult thing to control at times. Love can lead people to make very controversial decisions, and revenge works in very much the same way. Regardless, one cannot control whom he or she falls in love with. That said, he or she cannot control (at times) what will be done to protect the love. When that love goes astray, the person can feel that nothing is left. When nothing is left, there is nothing to lose. Medea most likely felt as if she had nothing to lose.
One could argue that Medea is not accountable for her actions if the Gods or Fates have influenced the course of her life and are acting through her.
I don't want a grand life for myself—
just to grow old with some security. 150
They say a moderate life's the best of all,
a far better choice for mortal men.
Going for too much brings no benefits.
And when gods get angry with some home,
the more wealth it has, the more it is destroyed. 
[Enter the Chorus of Corinthian women]
Here Medea desires the moderate life commended by the Gods. However, her husband does not have the same desires and chooses to unfaithfully enter a relationship with another women for political advantage. Jason has angered the Gods, and in this manner Medea could be an instrument for executing a kind of divine or fated justice.
Similarly, it was her husband Jason who was unfaithful.
That's when life is most secure and safe,
when woman and her husband stand as one. 20
But that marriage changed. Now they're enemies.
Their fine love's grown sick, diseased, for Jason,
leaving his own children and my mistress,
is lying on a royal wedding bed.
He's married the daughter of king Creon,
who rules this country. As for Medea,
that poor lady, in her disgrace, cries out, 
repeating his oaths, recalling the great trust
in that right hand with which he pledged his love.
Here Medea is not the individual whose behavior led to a lack of security and stability within her kingdom. Furthermore, her behavior could be seen as commendable because she was a character of action rather than a passive female character who would be owned and governed by a man.
Medea goes as far to take the lives of her own children. While repulsive and cruel, this action is also symbolic. Much of Jason's political power lay in the perpetuation of his lineage which was ensured through his marriage to Medea. Because Jason destroyed their marriage, Medea also, in a strange way that once again could be argued as a twisted act of fate or justice, destroys the products of that marriage as well.