Othello is certainly a tragedy by every definition of the word. In the most basic and commonplace sense, it is the story of terrible events, ending in violent death. A newspaper reporting on the carnage involved, particularly the murder of the innocent Desdemona, might legitimately describe the events of the play as tragic. Beyond this, Othello is a classical tragedy according to the criteria set forth by Aristotle in the Poetics. A great man of noble character, Othello, falls from a high position through his tragic flaw (in this case, jealousy) and in the process gains self-knowledge and understanding of the world around him. The audience experiences pity and terror at the sight of this fall, leading to the purgation of these emotions in a process Aristotle calls catharsis.

Othello is also a prime example of Renaissance tragedy and, of course, Shakespearean tragedy. A.C. Bradley, one of the most influential critics of Shakespeare in the early twentieth century, named it as one of the four great tragedies, alongside Macbeth, Hamlet and King Lear in his classic study Shakespearean Tragedy (1904). Renaissance tragedy follows the basic conventions of classical Aristotelian tragedy but tends to have a more complex structure, involving subplots and comic relief, as is the case with, for instance, the intrigues between Iago and his dupe Roderigo in Othello. The great Shakespearean tragedies follow the conventions of Renaissance tragedy, but tend not to rely so much on sensationalism and gore for their effect.

Literature can fall into two very broad categories: comedy and tragedy. A comedy does not have to be funny, although it can be. However, it does have to have a happy ending. In the most general sense, a happy ending means that none of the characters die at the end or have something terrible happen to them, such as becoming disabled. In a tragedy, the plot has an unhappy ending. This almost always means one or more of the main characters ends up dead.

Some of Shakespeare's plays could go "this way or that way," meaning a slight alteration of the plot could change them from comedy to tragedy or vice versa. For example, if Romeo had gotten the message telling him Juliet's death was faked, the story could have had a happy ending, and even Mercutio's death could have been absorbed into a joyous plot. Conversely, in A Midsummer's Night Dream, if the fairies had not interfered, Demetrius and Lysander could have fought each other to the death over Helena, and the play would have ended tragically, not comically.

Likewise, Othello could have ended happily if Othello had either seen through Iago or trusted Desdemona more. However, middle-aged and insecure about his ability to be lovable to a woman, Othello's own blind spots allowed an evil man to manipulate him into destroying himself and the woman he loved. Othello is a classic tragic hero, a good, honorable man with a fatal weakness. 

Othello is a tragedy because it meets the definition of tragedy in such standard authorities as Aristotle. Aristotle defined tragedy as a story about something that is "serious, complete, and of a certain magnitude" that uses drama to tell of the fall of someone highly placed. This fall occurs because of external or internal forces, especially the chief character's own "error or frailty," his or her "tragic flaw," and the drama ends with the attainment of understanding and a resolution of the fear and pity that it induces.
Othello fully satisfies this definition. Othello himself is a high, admirable character whose downfall arouses pity and fear. He and the other characters in the play are true to life, consistent, and behave logically according to the information they are supposed to have. Their characteristics support the plot -- Othello is jealous (his "tragic flaw") and trusting, Desdemona loving and faithful, Iago evil and devious, plotting the ruin of his supposed master Othello. Othello is brought down due to an external force (the hatred of Iago) working in harmony with his own jealousy, his tragic flaw, to end in his destruction and that of his wife, an equally admirable character. The incidents of the plot arouse pity and fear in the viewers; the situtuation (betrayal by a trusted associate) is universal, and so viewers can envisage themselves tricked in the way Othello is tricked. Finally, the play ends with a katharsis or "purging," a resolution of the pity and fear we feel at seeing Othello tricked into murdering his wife, as Iago is discovered and condemned and Othello fully understands what has been done to him and commits suicide.

Yes, "Othello" is a tragedy. Shakespeare wrote thirty- seven plays; of those 37, twelve of them are labeled as tragedies, most including "Othello" had been written between 1601 and 1608.  A Shakespearean tragedy has a few characteristics.  First, the main character(s) or protagonists must have a tragic flaw that will bring about his/her final demise yet must also possess characteristics that allow the audience to feel admiration or sympathy for him or her.  At the same time, this must be a character that is not completely pure at heart and "goog" but must possess some type of evil in his/her character.  The character of Othello in the play possesses these traits.  Because of the underlying themes in the play (those of love, jealousy because of love, and murder because of that jealousy), some people would call the play a romantic tragedy, but it is considered a Shakespearean tragedy, nevertheless.