These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Academics and tropers are split over the play. Either Romeo and Juliet were in love, but died due to rushing into things and a lot of bad luck, or Romeo just wanted to get into bed with her, or Juliet was looking for a way out of marrying someone she doesn't like and out of her controlling family and Romeo happened to be that way. As far as most of the modern audience is concerned, it's the first one.
It could also be argued that what Romeo and Juliet thought was true love was in fact just romantic infatuation intensified by Forbidden Fruit.
Friar Lawrence. Is he a kindly man of God, trying his best to help the two lovers live happily ever after? Or a Manipulative Bastard who knows full well how dangerous his plans are, but wants peace in his city and is willing to risk two children's lives for the greater good?
Cliché Storm: Even when it was written, the story had been told in various other forms.
Designated Villain: We're not supposed to like Paris because he stands between Romeo and Juliet. He was courting Juliet in the manner customary of the time, and is the only character who is killed without doing anything to deserve it.
In the 1996 version, almost literally, as he's dressed in tight-fitting black pants, with sharply tailored jackets and... very tight vest tops.
Ensemble Darkhorse: Mercutio, who has all the good lines in the early part of the play, making it more jolting when he's killed.
Arguably, Benvolio too, who seems to have found some standing amongst young people who value sanity over romance.
On a similar note, the Friar. In his first appearance, he scolds Romeo for falling for a girl he just met, while completely forgetting about the girl he was talking about two days ago. In his next appearance, he calls out Romeo for whining, and tells him to suck it up and look on the bright side.
The Nurse is also a well-liked character with some great lines. Doubly so if the actress playing her is a Large Ham.
Fan-Preferred Couple: Benvolio/Mercutio and Benvolio/Rosaline are both quite popular, despite never really being implied in the text.
Foe Yay: Between Romeo and Tybalt. "The reason that I have to love thee," indeed...
Idiot Plot: Mercutio, Tybalt, Romeo, Capulet, Juliet, Balthazar and Paris make some very bad decisions in this play. It might actually be more convenient to list the characters who aren'tToo Dumb to Live.
Iron Woobie: The Nurse. Despite having lost her husband, daughter, surrogate daughter and very close kindsman, she is possibly the least angsty character in the play.
Moral Event Horizon: Tybalt crosses it by killing Mercutio with a cheap shot, thus setting off a chain of events leading directly to the Downer Ending. This is softened in some adaptations, including the Zeferelli version, where Tybalt kills him accidentally while trying to knife Romeo (who was trying to intervene) and is somewhat horrified upon realizing who he had wounded.
Older Than They Think: It was not uncommon for Shakespeare to "borrow" his plots from other works. The story of Romeo and Juliet was heavily based on a poem by the English poet Arthur Brooks called The Tragical History of Romeus and Juliet. Brooks in turn got the story from a number of Italian and French novellas about Romeo/Romeus and Juliet/Julietta/Giulietta. These works bears many similarities to the story of "Pyramus and Thisbe" in Ovid's Metamorphoses.
Some Anvils Need to Be Dropped: A very short one in Romeo and Juliet, but Romeo drops an important point when he's at the apothecary and is paying the poor shopkeeper-money makes more people die than poison, and is just as bad, if not even worse, than poison.
There is thy gold, worse poison to men's souls,
Doing more murder in this loathsome world,
Than these poor compounds that thou mayst not sell.
Unintentionally Unsympathetic: For some, it's hard to feel sorry for Romeo and Juliet at the end of the play, considering that their misery is partially their own fault.
Values Dissonance: Juliet is only thirteen and already getting married, not to mention her parents are trying to push her into an Arranged Marriage (whether she wants it or not). Whilst the brawls and murders is treated with some gravity, the idea that characters would be easily carrying swords around and killing each other off at the drop of a hat would, likewise, be unthinkable today.