Peer Pressure
The main theme of the movie also sets up the entire plot; Danny and Sandy met when none of their friends were around and fell in love; yet around their friends, they feel the weight of peer pressure to conform to the image that they have carefully cultivated. Therefore, after the initial joy of seeing Sandy again at Rydell High, Danny reverts to his standard cool, stand-offish, don't care persona. He knows that his friends will laugh at his more romantic side and so he hides it, which actually ends his relationship.
Similarly, Rizzo is also in the same boat as Danny. She has an even harder-edged demeanor than he does which hides a sensitive and lonely girl underneath. Rather than welcoming Kenickie's help and his love, she rejects him because she does not want to be seen as a softer, nicer person than her peers expect.
Sandy also succumbs to peer pressure when she goes to Frenchy's house for a slumber party, trying smoking and drinking for the first time, and also getting her ears pierced in Frenchy's bathroom. Peer pressure has made it perfectly clear to Sandy that she is far too clean cut and pure for their group and so she makes changes to herself in order to fit in.
Love and Romance
This is, above all, a movie about love, centered around the love story of seemingly mis-matched teens Sandy and Danny. The path to true love is not smooth, but in the end both decide that it is worth making changes to themselves if it means that they become a more desirable person to the other. This is also the irony of love; they both change, and so they are still mismatched, but this makes them perfect for each other because they have learned the important lesson that love is unselfish.
There are also peripheral romances between the other characters in the film, varying in their intensity, but all coming together nicely, Cinderella style, at the end of the film.
Gossip
Gossip is dangerous and this film highlights this particularly well in the way it shows the issue of Rizzo's feared pregnancy. She tells Marty, and asks her to keep her confidence, but Marty tells her date, who tells Kenickie, and in the meantime, everyone from Rydell High finds out that Rizzo might be pregnant. She is then shunned as the bad girl. Nobody at the school actually knows for sure what is going on, but this does not stop them spreading assumptions and rumors throughout the school.