The Tragedy of Othello, the Moor of Venice is a "tragedy" alright, and not just because the word "tragedy" appears in the play's title. We've got a handy list of the features and conventions that are so common in this genre, so let's take a look, shall we?
Dramatic work: Check. And by "Check," we mean that, yes, Othello is a "play."
Serious or somber theme: Hmm. Othello's a study of the consequences of jealousy and racism, so check.
Hero's got a major flaw of character or conflict with some overpowering force: Check. You've probably picked up on the fact that Othello's a guy with a serious flaw (insane jealousy). Not only that, but Othello's also gullible – it doesn't take much for Iago to convince Othello that Desdemona's cheating on him (even though she's not). This, as some literary critics have argued, may have something to do with 1) Othello's suspicion that all women are inherently promiscuous and/or 2) Othello's fear that he, a black man, is not good enough for his white wife. Check out our theme discussions on "Race" and "Gender" for more on this.
Hero is destined for destruction and downfall: Check – sort of. The important thing to remember is that Othello experiences a major, major downfall over the course of the play. He starts out as a pretty noble guy – he's a celebrated war hero, he's obviously overcome quite a bit in order to reach the rank of a military general, he's respected by the Venetian government, he's a loving husband who has snagged a great wife, he's an eloquent storyteller (kind of like Shakespeare), and so on. By the end of the play, Othello's an irrational, violent, and insanely jealous husband who murders his own wife. Yet, while the idea of "destiny" plays an important role in plays like Macbeth and Hamlet, it's not really a factor in Othello. Some critics have argued that Othello's downfall is the "inevitable" outcome of Iago's masterful scheming and/or the racism Othello is subjected to in the play, but "destiny" doesn't seem to have much of a role here.
*Shakespearean tragedies always end in death but with some promise of continuity: Not all tragedies end in death, but all of Shakespeare's tragedies do. By the time we reach the end of the play, Othello has strangled Desdemona, Iago has killed Emilia, and Othello stabs himself in the guts. But, not everyone on stage is left for dead – Lodovico promises to return to Venice, where he will relate the tragic story of what has just happened to his countrymen. This is similar to what happens at the end of Hamlet, when Horatio promises the young prince that he will tell Hamlet's story to the world.
Othello's influence can also be seen in modern day psychological suspense thrillers (think writer James Patterson or film director Stanley Kubrick) because the entire momentum of the play is based on the twisted mind games of two (and often more) characters.