Was Macbeth the greatest tragedy ever written? Maybe. But before we go throwing around words like "greatest," lets take a peek at our handy-dandy tragedy checklist:
Dramatic work: Check. Macbeth's a play, that's for sure.
Serious or somber theme: The play's all about what causes people to commit evil acts (like murder). So, check.
Hero's got a major flaw of character or conflict with some overpowering force: Check. Macbeth's got some serious ambition (so does his wife), which makes him willing to kill in order to secure his position as King of Scotland. Plus, once Macbeth eliminates Duncan, he can't seem to stop killing people. Is there some other "overpowering force" at work too? Keep reading.
Hero is destined for destruction and downfall: Here's where Shakespeare mixes things up. On the one hand, the "weird sisters" (three witches) prophesize that Macbeth will become King of Scotland. "Weird" comes from the old English ("wyrd") word for "fate" (see these ladies' "Character Analysis for more about that), which aligns the witches with the three fates, who are supposed to control man's destiny.
So, does that mean the witches control Macbeth's fate? If the answer to this question is yes, then Macbeth is destined to murder Duncan, become king, and get then later get his own head lopped off by his disgruntled countryman. But this isn't necessarily the case. In fact, the play goes out of its way to dramatize Macbeth's deliberation about whether or not he should kill the King. What's more, the three sisters never say a word about murder. Are the weird sisters just a catalyst for the murderous ambition that's maybe been inside Macbeth all along? There's lots more room for interpretation here so go ahead and take a stab at it.
Ends in death but with the promise of continuity: Not all tragedies end in death but all of Shakespeare's tragedies do. The question isn't whether things will end badly, but how badly. In Macbeth, it's pretty bad—Macduff's entire family is murdered, along with Banquo and his son, and, of course, Macbeth himself.
But despite the deaths of individuals in the play (King Duncan, the guards, Macduff's wife and kids, Lady Macbeth, the Siward's son, etc.), Shakespeare is also interested in the restoration of political order. With Malcolm on their thrones, things (we hope) are going to get back to normal—culminating in Shakespeare's very own king James I, who traced his lineage back to Banquo.
So there you have it: Macbeth is definitely a tragedy. Is it the greatest ever written? At the least, it's a strong contender.