This is my father's favourite of Shakespeare's plays, and having seen the new production (in contemporary setting) at the National Theatre yesterday & knowing my dad, I can see why (I read the play a few years ago).
It is the story of a lying villain, Iago, whose motivation is pure malice and hatred of his Black boss, the honoured general Othello. Against the latter's nature he is made jealous of his young White lieutenant Cassio.
Apart from that of the raving racist Brabantio, the prejudice against Othello is as subtle and insidious as racism is today. His second-in-command feels he should have the general's place and uses White supremacy to undermine him out of spite.
Patriarchy is another issue in the play; Desdemona is passed as a chattel from father to husband, each feeling inclined to dispose of her at his will. In the conversation she has with Iago's wife Emilia, the latter expresses quite a strong feminist idea
"... Let husbands know
Their wives have sense like them: they see and smell
And have their palates both for sweet and sour,
As husbands have. What is it that they do
When they change us for others? Is it sport?
I think it is: and doth affection breed it?
I think it doth: is't frailty that thus errs?
It is so too: and have not we affections,
Desires for sport, and frailty, as men have?
Then let them use us well: else let them know,
The ills we do, their ills instruct us so."
So, not only is Othello a well structured play, with an engaging cast, powerful speeches and immortal lines; it's also one of the most stingingly 'relevant' of Shakespeare's works.