This is all a little rough since I did mine end of last year but here's the ones that were stressed to us to remember:
Thick lips - easy to remember, said p much every scene - good for racism, prejudice
The green eyed monster quote (Scene 3, Act 3) - good for jealousy, Othello/Desdemona, dangers of love, Iago
Reputation is an idle and most false imposition, oft got without merit and lost without deserving - Act 2, scene 3 - good for questions about reputation, rumours, lies,
Whatever you can from Emilia's speech, really. Every line is probably a paragraph's worth of analysis (4.3.84-103) - good for husbands and wives, feminism, female characters
She lov'd me for the dangers I had pass'd, And I lov'd her that she did pity them (act 1, scene 3) - Othello/Desdemona, reality vs illusion
Hope this helps!