Fate and coincidence are both themes which are established from the outset and continue throughout the play. The Chorus which, in effect, summarises the play and reveals the ending before the play has even begun, speaks of Romeo and Juliet being ill-fated. They are described here as "death-mark'd" and "star-cross'd" - the latter of which is referring to the belief at that time that the stars governed what happened; therefore to be "star-cross'd" would suggest that one was doomed.
Coincidences of timing and actions play a huge part in the plotline - in particular when it comes to the deaths of the ill-fated pair. If Romeo had received the letter telling him that Juliet was not dead then neither would have died (at that point) and may have been able to have relationship by making their respective families see sense.
The receipt of a single letter seems unimportant but it is what ultimately leads to Romeo's death which in turn leads to the death of Juliet. This can be attributed to a theory known as "The Butterfly Effect" which theorises that the fluttering of a butterfly's wings on one side of the world can cause a natural disaster such as an earthquake on the other side of the planet.
Ultimately it seems to be fateful that their love will not withstand the constant feuding between their families, however what does not seem completely fateful is that both (or even one of) the lovers will die. It is fair to say that both die as a result of their quarrelling families. This, in my opinion, is ironic that the two individuals capable of bridging that Capulet-Montague gap are the two that die. Perhaps even more ironically their death is the one thing which seems to bring the families together.
Personally I believe that a great deal of what takes place in the story can be attributed to fate and coincidence but there are parts of the story which appear to rely on neither fate nor coincidence.