What inspired Shakespeare to write Romeo and Juliet?

One of the frustrations for Shakespeare scholarship is that while there are a wealth of legal documents pertaining to him, from marriage certificates to contracts to wills, we have a nary a word (outside of his poems and plays, which are obviously open to interpretation) of personal documentation explaining how or what he thought and felt. There's not one personal letter nor a scrap of a diary account. Therefore, what inspired Shakespeare to write Romeo and Juliet must remain speculative.
That being said, he is believed to have been aware of a poem published by Arthur Brooke called The Tragicall Historye of Romeus and Juliet. This, along with his knowledge of Ovid's story of the ill-fated lovers Pyramus and Thisbe probably inspired the idea of a basing a play on this theme.
Shakespeare wrote Romeo and Juliet early in his career and not long after A Midsummer Night's Dream, so it may well have lodged in his mind that he wanted to expand the comical Pyramus and Thisbe production of the rude mechanicals in Midsummer into a longer, more serious treatment. Love is clearly on his mind at this period of his development.
One thing we can surmise from the care Shakespeare took in having his sonnets published versus his complete disinterest in publishing his plays is that he was in playwriting mostly for the money. Therefore, he must have felt there was a market for a tragic love story when he wrote Romeo and Juliet. He would no doubt be more surprised than anyone to find that his lasting reputation is based primarily on his plays and not his poetry.

The narrative of Romeo and Juliet is one of the most ancient human stories there is: the tale of tragic lovers. The primary source for Shakespeare's story seems to have been "Pyramus and Thisbe," an ancient Greek myth about lovers whose families loathe each other. Their story is preserved in Ovid's Metamorphoses.