In Romeo and Juliet, I honestly disliked a huge majority of the characters, but I do like Rosaline. I know she didn't have any lines, and she was only mentioned a few times, but I believe she did have an impact on this play. Rosaline is Romeo's love interest in the beginning of the play and the reason Romeo is so upset, claiming he will never love anyone else. If Rosaline hadn't been in the play it is highly possible Mercutio and Benvolio would not have brought Romeo to the Capulet's party to cheer him up.  If Romeo didn't go to the party then he and Juliet would not have met, and we can make the assumption that no one would be dead.
          Also, Rosaline plays an important part in characterizing Romeo's immaturity and moody nature.  He drops his love for her so quickly, showing that he is both impulsive and not entirely serious. So as you can see Rosaline plays an important part in Romeo and Juliet.