Romeo and Juliet's origins are not real events but on a 1562 poem by Arthur Brooke titled The Tragical History of Romeus and Juliet. The plot of the original poem is much the same as Shakespeare's play: two young lovers from rival families fall in love, then commit suicide when their plans are thwarted.
Of course, other early works influenced Shakespeare's adaptation, such as the Greek tale of Pyramus and Thisbe. The story of Romeo and Juliet as Shakespeare would have known it dates back to the early sixteenth century and was written by an Italian named Luigi Da Porto, who was allegedly inspired to write the tale based on an unrequited love he harbored for a teenage girl in his youth. However, that is not enough to qualify Romeo and Juliet as being based upon a true story. And it must be noted that Shakespeare likely first encountered the story through Brooke, not Da Porto.
There are some key differences between the two versions. Firstly, Brooke's story takes place over a few months, while Shakespeare crams Romeo and Juliet's meeting, marriage, and double suicide into a few days. Brooke's Juliet is eighteen, while Shakespeare's is thirteen. The ending of Brooke's play has the Nurse banished and the apothecary who sells Romeo the poison hanged, adding a more moralistic tone to the story than Shakespeare, who only assures us through the words of the Prince that "some shall be pardoned and some punished."