It is, of course, Iago's revenge that provides the catalyst for virtually everything that happens in the play. It is his deep resentment at his relatively low status in life that drives him on, making him determined to destroy all those, including his master Othello, who represent a social system which has held him back all these years.
Iago's thirst for vengeance is all the more dangerous in that it shows no signs of being assuaged. There's something positively demonic about it; the desire for revenge controls Iago to such an extent that it's doubtful he could break free from its iron grip even if he wanted to.
As for forgiveness, a particularly heart-rending example comes when Desdemona forgives Othello with her dying breath:
Nobody. I myself. Farewell.
Commend me to my kind lord. Oh, farewell! (Act V Scene ii).
The man who's just murdered her in a fit of jealous rage, a "kind lord?" Desdemona's capacity for forgiveness is remarkable indeed though it does render her somewhat suspect in the eyes of successive generations of feminist critics who've interpreted Desdemona's dying words as indicative of a weak and pliable character.