What impact does Romeo have on the tragedy in Shakespeare's Romeo and Juliet?

Although Shakespeare, in Romeo and Juliet, wants the audience to believe fate is the primary culprit in the final outcome, Romeo exacerbates the tragedy and has a major impact on events with three important decisions.

First off, he rushes into the relationship with Juliet. Within an hour of meeting the girl he is asking her to marry him. Even Juliet realizes they may be going too fast. She advises him to wait and see if he feels the same way when they meet again. She says in Act II,

I have no joy of this contract tonight.
It is too rash, too unadvised, too sudden,
Too like the lightning, which doth cease to be
Ere one can say “It lightens.” Sweet, good night.
This bud of love, by summer’s ripening breath,
May prove a beauteous flower when next we meet.

Despite Juliet's misgivings, Romeo will not be dissuaded. He asks her to marry him and she is too much in love to refuse.

Probably the decision which most sets up the tragic ending is Romeo's rash decision to seek revenge against Tybalt in Act III, Scene 1. Mercutio is killed, partly because Romeo tries to interfere in the sword fight between Mercutio and Tybalt. Once Mercutio dies, rather than keep his head and consider the Prince's edict about fighting from earlier in the play, Romeo challenges Tybalt and kills him. The decision leads to mischief, as he is banished and Juliet is forced to take a sleeping potion which will render her lifeless after her parents decide she should marry Count Paris.

The third unfortunate decision comes in Act V after Balthasar gives Romeo the news of Juliet's supposed death. Romeo plunges headlong into a plan for suicide. He bribes an apothecary to sell him poison and then hastily heads to the Capulet tomb. He even kills Paris, who is there to pay his respects to Juliet. Romeo never consults the Friar or stops to consider his decision. He is absorbed by his love and sorrow. If Romeo had waited just a few more minutes, he may have gained the time which Juliet needed to wake up from the effects of the potion.