I would say that a key characteristic of Romeo and Juliet's relationship is that it is powerful. In the beginning of the play Romeo is pining for Rosaline. He is basically being a whiny teenage boy who can't be with this girl he really likes. Granted, it is because she took a vow of chastity, but that does not change Romeo's sappy lament to Benvolio.
The reason I say Romeo and Juliet's relationship is powerful love is because of what it drives them to do. To the two star crossed lovers, their relationship is more important than their relationships with their families. This can be supported by Juliet's line: "Deny thy father and refuse thy name, or if thou wilt not, be but sworn my love, and I'll no longer be a Capulet." Their love is more important than long time friendships, as illustrated when Romeo bails on Mercutio and Benvolio to be with Juliet. Romeo even comes back to try and be with Juliet after being banished by the government.
The power of love in their relationship is the cause of the play's tragic end as well. They both love each other so deeply that they each can't bear the thought of living without the other.
Another characteristic of their relationship is that it is based on the concept of love at first sight. They meet, they instantly fall deeply for each other, and die in other's arms. That could lead to another characteristic of their feelings for each other. They both believe that love is eternal and that there is a single "one and only."