One common element is the idea of the underdog or the ordinary person falling in love with someone extraordinary. For example, in many shoujo anime and comics, the female lead might be an average girl who falls for a popular or talented boy. Another element is the use of obstacles to test the relationship, like family opposition or a rival in love.
Well, a lot of comics and anime love stories involve the growth of the characters. The love they experience helps them to become better versions of themselves. Take 'Fullmetal Alchemist' for example. While it's not a pure love story, the relationship between Edward and Winry has elements of this. As they grow up, their feelings for each other change and develop. Another common element is the setting. Whether it's a high - school setting like in many shoujo and shounen works, or a fantasy world, the setting often adds to the charm of the love story.