In Othello, Othello is light years ahead of his time in terms of his character being noble. Could a former slave, pagan, black Moor be made general of a white, Christian city-state's armed forces? I think not. As a black man nearly twice her age, could he be allowed to marry the young Senator's only daughter? Again, I think not. The very fact that the character makes it to the stage and is presented, against all odds, as a fine general and a good husband in Act I is incredibly noble.
Secondly, tragic heroes are, by definition, noble. According to Aristotle, nobility is that the first mark of a tragic hero. Enotes says:
(According to) Aristotle's Poetics it is imperative that the tragic hero be noble.
Othello is very noble in Act I, but he reverts from it as the play goes on. After Othello testifies of his love for Desdemona before the Senate, the Duke says:
This means that if he had a daughter (and maybe he does), Othello would win her over and he, her father, would consent to the marriage. That's how noble Othello is: he can woo the maids and their fathers of high rank.
Even Othello's sworn enemy, the man who vows revenge against him for having relations with his own wife, Iago, thinks he is noble in Act II:
But, in Act III, Othello begins to loose his nobility to jealousy. Desdemona admits that although Othello is jealous, he is noble:
Is this the noble Moor whom our full senate
Call all in all sufficient? Is this the nature
Whom passion could not shake? whose solid virtue
The shot of accident, nor dart of chance,
Could neither graze nor pierce?
Iago responds, "He is much changed."
Overall, Othello begins noble, but jealousy corrupts him and he dies a victim of Iago's deception and his own titanic passions.