Shakespeare's Romeo and Juliet is actually widely thought of as a "Problem Play." While the play ends in tragedy, it actually begins comically (Snyder, "Review: "Romeo and Juliet: Comedy into Tragedy.").
A tragedy generally focuses on one tragic hero who reaches his demise as a result of a fatal character flaw, as we see in Macbeth or Hamlet. The play reveals the character's innermost thoughts and feelings. While the character dies as a result of the fatal flaw, the reader/viewer does not think that the character's fate is wholly deserved.
Of course, one way that Romeo and Juliet diverges from Shakespeare's classic tragedies is that it focuses on a couple rather than one person. We do see more of a focus on Romeo in that the play begins with Romeo and ends with Romeo in that his death speech is far longer than Juliet's, but for the most part it focuses on both characters equally.
Another way that the play diverges from Shakespeare's other tragedies is that fate has a far larger role in their deaths than in his other tragedies. We do see character flaws in both Romeo and Juliet, especially rashness, impetuousness, and the reliance on uncontrolled, violent, passionate emotions rather than rational thought. However, these character flaws alone do not necessarily lead to their deaths. Instead, the fact that they are both born into feuding families leads them to their deaths--families who also act rashly, impetuously, and with violent, uncontrolled emotions. Hence, unlike other tragedies, fate plays the larger role in their deaths rather than tragic character flaw.
Shakespeare's comedies, on the other hand, actually do focus on pairs of lovers, just like the characters Romeo and Juliet. Also, in comedies, the young tended to try and outwit the older generation (Dr. Schwart, "Shakespeare's Plays: Comedy"). We do see a little bit of that in the opening act of Romeo and Juliet, especially when we see Benvolio and Mercutio decide to crash the Capulet's ball. Shakespeare's comedies had "stock characters" used expressly for amusement, such as jesters, fools, and "female confidents" (Dr. Schwart, "Shakespeare's Plays: Comedy"). Mercutio is one character that has many comical elements. Also, the Nurse is used expressly for comic effect and serves as Juliet's "female confident." Finally, comedies end in happy unity, and while it is true that Romeo and Juliet both die, the two families do unite in the end (Dr. Schwart, "Shakespeare's Plays: Comedy").
Hence, we see that while Romeo and Juliet ends in tragedy, it begins as a comedy and has an ending of unity much like comedies. Therefore, Romeo and Juliet is neither entirely a tragedy, nor entirely a comedy, but rather a "Problem Play."
Yes, it meets the criteria of literary tragedy. The protagonists make life decisions based on emotions. They are well rounded characters the reader can feel empathy for. most importantly, they suffer because of their choices.