There are many different films that can relate to Romeo and Juliet. I think that many Bollywood films operate on the premise of "star-crossed lovers," even if their endings might be a bit different. There's also the animated comedy Gnomeo and Juliet.
West Side Story is one of the most relatable films because its context is warring gangs in New York City. The Jets and Sharks are modern counterparts to the fair houses in Verona. In some respects, Casablanca features the idea of people in love who cannot be together. While Ilsa and Rick are not socially divided as Juliet and Romeo, both sets of lovers are unable to be with one another as a result of the world around them. In the same way, The Notebook represents two people in love who are unable to remain happy together. Social stratification and Alzeheimer's go very far in dividing two people who know that they are in love with one another. This idea can be seen in The English Patient, another narrative where people who are meant to be with one another are unable to pursue their passions to a happy end. Shakespeare's construction of love and its pain has been echoed in many modern films. As a result, there are different films that can relate to Romeo and Juliet.
Because Romeo and Juliet is a tragedy more than it is a romance, given that the young lovers both die rather than negotiate the social pressures to unite as an exemplar for the society in which they live, the film version of West Side Story (1961) is still one of the best movies through which to understand the dynamics of the play. With the turf war of the Sharks and Jets reflecting the feud separating the Capulets and Montagues, viewers can see both the pressures and inevitably fatal violence that comes to tear apart the burgeoning romance between Maria (Juliet) and Tony (Romeo).