What are some quotes from romeo and Juliet that show the theme people will do whatever is necessary for someone that they really love?

Probably this particular sentiment is best shown in Juliet's response to Friar Lawrence in Act IV Scene 1:

O, bid me leap, rather than marry Paris,

From off the battlements of yonder tower;

Or walk in thievish ways; or bid me lurk

Where serpents are; chain me with roaring bears;

Or shut me nightly in a charnel-house,

O'er-cover'd quite with dead men's rattling bones,

With reeky shanks and yellow chapless skulls;

Or bid me go into a new-made grave

And hide me with a dead man in his shroud;

Things that, to hear them told, have made me tremble;

And I will do it without fear or doubt,

To live an unstain'd wife to my sweet love.