All of these men are killed needlessly and as a result of blind, emotional rage. The progression of these killings also indicates the cumulative effect of the hatred these warring groups feel towards one another, despite the fact that no one can really recall any practical reason for the feud.
Mercutio is slain by Tybalt during a fight between the Capulet and Montague clans and their friends. Romeo kills Tybalt in anger, in retribution for his best friend Mercutio's death. Paris, who is betrothed to Juliet, is then slain by Romeo when he enters Juliet's tomb to lay flowers for her (thinking she is dead after she has taken the sleeping draught), and Romeo believes he is there to desecrate the tomb. In every case, each murder is borne of the passionate hatred generated by the Capulet-Montague feud.
The obvious link is that Romeo is involved somehow in all three deaths. Romeo kills Tybalt after Tybalt kills Romeo's best friend, Mercutio. As Tybalt and Mercutio are fighting, Romeo steps between them, and Tybalt fatally stabs Mercuto under Romeo's arm. Romeo kills Paris at Juliet's tomb, not really knowing who Paris is or why he would be visiting Juliet in the first place. Romeo's immaturity and haste are responsible for all these deaths. If Romeo had not gone to the Capulet party, Tybalt would never have been outraged, meaning Tybalt would not have issued the challenge on Romeo's life. If Romeo hadn't rushed between Mercutio and Tybalt, Mercutio would not have been distracted enough to leave himself vulnerable to Tybalt's sword. If Romeo had simply asked who the man visiting Juliet was, Paris might have lived. Romeo manages to victimize many characters in the play due to his own selfish reactions.
In addition to the information above, the deaths are also the result of impetuous behavior on the parts of all three young men.
Mercutio provokes Tybalt into a fight after Romeo refuses to be baited by Tybalt's goading. Romeo comes between the two and Mercutio is made "a grave man". Romeo's passion gets the better of him when his friend is killed and seeks vengeance upon Tybalt. His passion again comes into play against Paris, who was just paying his respects to his "dead" betrothed.
The saddest part is that Mercutio and Paris were not even members of the feuding families, but rather relatives of the Prince.
One could almost call Paris an "innocent bystander" due to his ignorance of the whole situation. He was not involved in the feud in any way other than as an observer and suitor for Juliet.