Romeo and Juliet are willing to sacrifice the influence of their families in order to be together. Both come from affluent backgrounds, and their families have a fairly solid rule when it comes to social interactions: avoid each other. This long-standing family feud has been pretty successful thus far in keeping them apart; as young adults, they don't seem to have ever noticed each other before.

But upon meeting, Romeo and Juliet are inexplicably drawn together regardless of what their families might think. Romeo is banished, and if he had lived and his plans had succeeded, he would have given up the comfortable societal position extending from his family in order to be with Juliet. When Juliet tells her father that she will not marry Paris, Lord Capulet's response is threatening:

CAPULET:

Hang thee, young baggage! Disobedient wretch!
I tell thee what: get thee to church o’ Thursday,
Or never after look me in the face.
Speak not. Reply not. Do not answer me.
My fingers itch.—Wife, we scarce thought us blest
That God had lent us but this only child,
But now I see this one is one too much
And that we have a curse in having her.
Out on her, hilding! (III.v.166-174)

This stands in sharp contrast to his loving tones toward Juliet early in the play. Both Romeo and Juliet are willing to sacrifice the prejudices of their parents as well as their favor in order to be together.

Juliet is also willing to sacrifice her chastity in order to be with Romeo, which was no small sacrifice in this historical context. Women who were found unchaste were dismissed from society and likely from any future potential matches, particularly in the upper echelons of society. While it is true that Juliet married Romeo before their sexual experience, she did so without her father's knowledge or blessing. The two of them have sacrificed the expectations of their society and have risked disastrous effects to their reputations for their hasty actions.

In the end, they sacrifice life itself to show the depth of their love—that they simply cannot go on living without the other.

Romeo and Juliet sacrifice everything—which is to say, their lives—in order not to have to live apart. Whether they will be together is a matter for theological speculation. They have done everything they can in the matter by getting married, an insoluble bond according to the Catholic Church, but neither mentions any hopes of an immortal reunion when they die.

The timescale of the play is so short that it is not entirely clear what they have given up for one another while its events are unfolding. The most serious sacrifices on each side appear to be Romeo's banishment in III.i and Juliet's parents disowning her in III.v. In the first case, however, one cannot say that Romeo kills Tybalt in order to be with Juliet. On the contrary, Juliet would much prefer that he had not done so. Juliet's estrangement from her parents is a direct consequence of her relationship with Romeo, but it does not last long once she pretends to be willing to marry Paris. Given the power and influence of the Montagues, we also have no idea how long Romeo's banishment would have lasted if he had remained alive.

Romeo and Juliet both endure danger in order to be together, but the circumstances of Mercutio's death, and Tybalt's, make it clear that Shakespeare's Verona is a dangerous place anyway. Romeo is probably in no more peril climbing into Capulet's orchard than he would have been stalking the streets looking for trouble with Mercutio. Romeo and Juliet, therefore, make no significant sacrifices before they make the ultimate sacrifice in the final scene.

Certainly, Romeo and Juliet both sacrifice much in their daring and "star-crossed" love.  For, they both abandon the safety and security that comes from being children of aristocrats in Renaissance Verona, Italy. Their impassioned love drives them to risk death on more than one occasion.

Indeed, by attending the masquerade held in honor of Juliet, Romeo challenges the edict of the Prince, who in the first scene of the play forbids the Montagues and Capulets to disturb the "quiet of our streets" under pain of losing their lives.  For, by entering the Capulet home, Romeo risks death at the hands of the fiery-tempered Tybalt, who identifies him.  Later, in the second scene of Act II, Romeo scales the walls of the Capulet orchard in the hope of again seeing Juliet; in so doing, he risks death if any of the Capulet servants notice him.  When she walks out onto the balcony, Juliet tells Romeo, 

How cam'st thou hither, tell me, and wherefore?
The orchard walls are high and hard to climb,
And the place death, considering who thou art,
If any of my kinsmen find thee here. (2.2.66-69)

Their subsequent pledge of love and hasty marriage also endanger the young lovers.  For, Romeo and Juliet have clearly sacrificed their security within their own families, and they both have risked the wrath of both of their families by this marriage. 

In Act III, therefore, the danger of their having married their enemies presents itself as Tybalt and Mercutio argue and the newly married Romeo attempts to intervene.  Pledging his love for Tybalt now as the in-law of the Capulets, Romeo raises the ire of Tybalt who is ignorant of this new development; he raises his sword and Romeo impedes Mercutio from defending himself.  This tragic action causes Romeo then to be banished from Verona by the Prince.  Thus, by marrying Juliet, Romeo has lost his very citizenship in the Verona community and must separate himself from his new wife.  So, he has to sacrifice any comforts he might have as the husband of Juliet.

With Romeo banished, Juliet finds herself in a situation which calls for self-sacrifice.  Since she cannot be with Romeo, her new husband, and she cannot marry the Prince as her mother and father desire, Juliet loses the security of her earlier life and must sacrifice her safety and comfort.  She turns to Friar Laurence and drinks his potion to forestall any marriage between her and the Prince.  With this potion, the friar plans, she will sleep as though dead; meanwhile the friar will talk with Lord and Lady Capulet, informing them that their daughter cannot marry Paris since she is already married.  However, the plan to notify Romeo in time goes awry and the two lovers despair; finally, they pay the ultimate sacrifice of their lives for the love of each other.