What is some important dialogue that furthers the plot in Shakespeare's Romeo and Juliet?
Dialogue that furthers the plot will introduce either a conflict or a theme, as the plot of a story revolves around its conflicts and themes. One good moment of dialogue is in Prince Escalus's speech threatening the lives of any Capulet or Montague who continues causing public brawls. The Prince's threat of capital punishment is seen in his lines, "If ever you disturb our streets again, / Your lives shall pay the forfeit of the peace" (I.i.92-93). This line is important because it portrays the conflict of man vs. society that Romeo later encounters. Romeo battles against being caught up in his family's feud, but he also battles against the Prince's law when he slips up and slays Tybalt for threatening his own life. Not only that, the Prince's line explains why Romeo is afraid of being sentenced to death after killing Tybalt, even though the Prince decides to show mercy and only banish Romeo instead.
Other important lines in this speech that also reveal a central conflict that is important for moving the plot forward is the Prince's reminder of how the public fights between the Capulets and Montagues are always started. We see this reminder in his lines,
Three civil brawls, bred of an airy word
By thee, old Capulet, and Montague,
Have thrice disturb'd the quiet of our streets. (I.i.85-87)
In this passage, the phrase "airy word" can be interpreted as referring to a "meaningless comment" and shows us that the Capulets and Montagues have no reason for starting the fights they start. Hence, this passage shows us the play's conflict of man vs. man, meaning Capulets vs. Montagues, and the whole plot revolves around this conflict.
Another good passage that drives the plot forward is spoken by Juliet immediately after she learns who Romeo truly is, as we see in her lines, "My only love, sprung from my only hate!/ Too early seen unknown, and known too late!" (I.v.147-148). This passage portrays Juliet's distress at learning that she has just fallen in love with one of her enemies. Hence, this passage helps move the plot forward by elaborating on both the conflicts man vs. man and man vs. fate. The only reason Juliet has to be distressed is that her family is involved in a feud, hence, the conflict of man vs. man is creating trouble for Juliet. Also, Juliet was unluckily born into a family who was warring with another family, therefore this passage also portrays the theme of man vs. fate that the play revolves around.