No spoilers to worry about here: as tragic as it is, the ending of Romeo and Juliet shouldn't surprise anyone. We're told from the get-go that our "star-crossed lovers [will] take their life" (Prologue). We also know that Romeo and Juliet belongs to the genre of "tragedy," and Shakespeare's tragedies always, always, always end in death. (You can read more about this by going to "Genre.) The point of reading or watching Romeo and Juliet isn't to find out what happens, but to watch it happen—and to feel some strong emotions along the way.
This is one of the most famous passages in the entire play, so let's take a close look, shall we? When Romeo and Juliet talk for the first time at the Capulet ball, Romeo uses his best pickup line: touching Juliet's hands and lips, he says, would be a kind of religious experience. (We've heard that before, haven't we? He used to say this kind of stuff about Rosaline.) Angling for a kiss, Romeo refers to his lips as a two "pilgrims" that would worship at a holy "shrine" (that would be Juliet's lips). A pilgrim, by the way, is a person on a religious pilgrim age to a holy place. Pilgrims were also called "palmers" because they often carried palm leaves on their journeys.
In response, Juliet teasingly puns on the word "palmer" to suggest that touching hands, "palm to palm," is like kissing (so Romeo, presumably, should be content with touching her hands instead of making out). But Romeo refuses to be shot down. Instead of walking away with his tail between his legs, he uses Juliet's hands=lips logic to argue that kissing the lips of Juliet (who has reached "saint" status by this point) would be just like praying, which involves placing ones palms together. Juliet seems playfully willing to go along with all this and allows Romeo to kiss her.
What's interesting is that, before Romeo can lock lips for a second time, Juliet says "you kiss by the book," which suggests that all of Romeo's moves (his pickup lines and even the way he kisses) are a bit scripted and cliché. So, Juliet's clearly smitten with Romeo but she also recognizes that Romeo isn't exactly original.
At the same time, however, the dialogue between Romeo and Juliet takes the form of a sonnet (up to the point where they kiss), which is incredibly romantic. So, while Romeo's moves are a bit predictable, we can also recognize that Romeo and Juliet's romance has the potential to be anything but conventional.
Romeo learns only of Juliet’s death and decides to kill himself rather than live without her. He buys a vial of poison from a reluctant Apothecary, then speeds back to Verona to take his own life at Juliet’s tomb. Outside the Capulet crypt, Romeo comes upon Paris, who is scattering flowers on Juliet’s grave. They fight, and Romeo kills Paris. He enters the tomb, sees Juliet’s inanimate body, drinks the poison, and dies by her side. Just then, Friar Lawrence enters and realizes that Romeo has killed Paris and himself. At the same time, Juliet awakes. Friar Lawrence hears the coming of the watch. When Juliet refuses to leave with him, he flees alone. Juliet sees her beloved Romeo and realizes he has killed himself with poison. She kisses his poisoned lips, and when that does not kill her, buries his dagger in her chest, falling dead upon his body.