Why is Tybalt to blame for the deaths of Romeo and Juliet?

In Act I, Scene 1, when Romeo comes on the scene after the street fight which opens the play, he makes the comment that, while the feud between the Montagues and Capulets is based in hatred, it has more to do with a love for fighting:

O me! What fray was here?
Yet tell me not, for I have heard it all.
Here’s much to do with hate, but more with love.

This statement is quite true of Tybalt, Juliet's cousin. He is one of the instigators of the street brawl and seems bent on perpetuating the feud in any way possible. His anger and aggression are one of the major causes which lead Romeo and Juliet to commit suicide at the end of the play.

In Act I, Scene 5, he overhears Romeo speaking at Capulet's party and, when dissuaded by Capulet from fighting Romeo on the spot, vows revenge and sends a letter of challenge to Romeo. In the meantime, Romeo falls madly in love with Juliet and they marry before Romeo ever hears of the challenge. 

In Act III, Scene 1, Tybalt acts on his challenge by seeking out Romeo in the streets. He first comes upon Mercutio and the two trade insults before Romeo enters. When addressed as a "villain" by Tybalt, Romeo immediately backs down because he has just married Juliet. He even suggests that he loves Tybalt. Of course, neither Tybalt nor Mercutio know of Romeo and Juliet's romance and they wind up fighting. Unfortunately, Romeo is unable to stop the sword fight and Mercutio is eventually stabbed by Tybalt who then runs away. Had the scene ended here, Romeo and Juliet may have continued their lives and eventually even announced their marriage and brought the families together just as Friar Laurence had hoped when he performed the marriage.

Despite having already killed one man, "the furious Tybalt" returns to the scene. Obviously, his love of fighting has not been satisfied. Feeling he has been cowardly and "effeminate," Romeo fights Tybalt and promptly kills him. It could certainly be argued that Tybalt's return, and his death at the hands of Romeo, lead directly to the mischief which occurs in the second half of the play. Lord Capulet, believing Juliet to be grieving over her cousin's death, arranges a "day of joy" by promising Juliet to Count Paris. This plan puts Juliet in a problematic situation and ends in her faking her death and the other circumstances which lead to the final suicides of Romeo and Juliet. Tybalt, playing out his role as the main catalyst of feud, is easily blamed for the final tragic events.