That is one of my favorite movies, because Julie Delpy's leading role is one of the most believable characters I've ever seen.
Most movies portray women as either virginal and aloof (Casablanca) or superhuman and independent (There's Something About Mary). In these movies, the men are the ones who make mistakes, who need help, and the women are angelic figures there to help out. The men are the characters who usually change.
In Before Sunrise, Julie Delpy and Ethan Hawke play equally complex characters, who commit equal mistakes in their past relationships, who are drawn to each other equally.
Julie Delpy is beautiful, of course, but not in the sense of the male ideal. She wears flat shoes, little make-up, and a plain dress, something much more attainable for the average young woman.
She buys Ethan Hawke a drink (women never pay in the movies, but it often happens in life) because he is traveling and only 23 years old, so he doesn't have much money. This is a true homage to Gen X reality.
It is partly due to the portrayal of this character that I find Richard Linklater, the director, so respectable. He paid women their due in this movie, creating a character that was neither a sexpot nor pathetic, but somewhere in between.