The question can be answered compellingly either way. The Chorus declares that Romeo and Juliet were "star-cross'd". Romeo refers to "some consequence yet hanging in the stars". After he kills Tybalt, he cries, "O I am Fortune's fool!" One can talk forever about the number of coincidences in the play.
However, the characters' own actions must account tor the tragedy, to a large extent. Romeo, in particular, is very impetuous, and his rash decisions (his quick change of heart about Rosaline, his determination to marry Juliet immediately, and his killing of Tybalt) have terrible consequences.
In the classical sense, there is no such thing as a tragedy of fate. Tragedy is the result of the choices of the characters in the play, the product of their personality flaws. But nowadays we take a more liberal view, and think of "tragedy" as any sad death, regardless of its cause or stature. However you answer this question, you will have plenty of evidence from the text to support your opinion.
I honestly think it was fate. There were too many things that happened to the couple that I do think "the star-crossed lovers" had to be together to matter what. If the servent was literate, Romeo would have stayed home to mope some more. Romeo would have returned to Juliet, banishment or not. It's part of his implusive nature. If it was free will, Juliet would have honored her parents' wish to marry Paris after the party.
As for evidence for this idea of this being a fated love, take a look at how the two describe their love. There are celestial bodies used as metaphors. You have to remember that many Elizabethans believed that all events in life were predetermined by some sort of higher power.
What kind of love did they have? An intense love, one that blasted past most social restrictions on it. Not all restrictions; they still wanted to be married, and they were still concerned with what their families' responses would be.
As far as fate vs. free will, that's a good question. I'd have to say it was fate. There are two reasons I'd say this. The first reason is simplest: in the prologue the chorus refers to them as "star-crossed lovers," suggesting their fate was written in the stars.
The other reason is more philosophical. If you had a choice about who you fell in love with, would you choose an enemy of your family?