Juliet cannot live without Romeo and is tormented by guilt at causing his death.
Juliet kills herself because the play is a tragedy. These two teenagers are very melodramatic. We are told in the beginning of the play, in the first prologue, that Romeo and Juliet are going to die.
From forth the fatal loins of these two foes
A pair of star-cross'd lovers take their life;
Whose misadventured piteous overthrows
Do with their death bury their parents' strife. (Act 1, Prologue)
Romeo and Juliet are both used to death. Their families have been feuding for so long that it is not unusual for swords to be drawn in the streets for the most minor of insults. Death is just a part of their everyday existence.
Ironically, the feud between their families brought Romeo and Juliet closer together. They loved quickly, passionately, and in secret. They had to keep their love a secret because it was forbidden. The bloodshed between their families would have been terrible if anyone found out.
Because Romeo and Juliet never had a normal relationship, everything was an extreme in their minds. They were immature, certainly, but their love burned like a fire. It was them against the world. All they had was each other, and all they needed was each other. This attitude led to extreme decisions.
This is the reason why Romeo was so tormented by the idea that he was banished. While others tried to convince him that it was no big deal, because at least he was alive, to him it was a tragedy. He could not stand to be away from Juliet.
If possible, things were even worse for Juliet. Her father insisted that she marry a man she did not love, who was older than her, and whom she barely knew. Her situation was untenable. She was secretly married to Romeo and her father would not relent about the marriage. She faked her death, thinking it was the only way she and Romeo could be together.
It was the worst thing she could have done. Once Juliet was lying in the tomb comatose, she lost control of the situation. Romeo was supposed to find out what happened and whisk her away. Instead, he found her and thought she was dead. Out of grief, he killed himself. When Juliet woke, it did not take a genius to figure out the situation. Her lover and husband was dead, and it was her fault.
Poison, I see, hath been his timeless end:
O churl! drunk all, and left no friendly drop
To help me after? I will kiss thy lips;
Haply some poison yet doth hang on them,
To make die with a restorative. (Act 5, Scene 3)
Juliet is overwrought with grief. She probably is also not thinking very clearly because she just woke from a stupor. Who knows that the effects of that potion were? She woke up, saw Romeo dead, and took her own life to end her suffering. What was the alternative? Should she marry Paris?
If Juliet had not killed herself, she would have had a lot of explaining to do. Why was Romeo there, dead? Why did she fake her death? Their parents were forgiving in their grief when they found both Romeo and Juliet dead, but who knows if they would have reacted the same way to learning what happened if Juliet was still alive to take the blame for it.