Often, there is the theme of fate. Sometimes, it seems as if fate is conspiring against the lovers, making their love impossible. Additionally, personal insecurities play a role. If a character has self - doubt or is afraid of commitment, it can turn love into an impossible situation. In many 'an impossible love novel', external circumstances like war or family obligations can also be themes that make love difficult or impossible.
One common theme is social class differences. In many novels, characters from different social classes fall in love, like in 'Pride and Prejudice' to some extent. Another theme is fate. Sometimes, the lovers are fated to be apart, as if some unseen force is preventing their union. For example, in some tragedies.
I would suggest 'Lolita' by Vladimir Nabokov. Although the theme is quite controversial, the love of Humbert for Lolita is an impossible one. It is not only because of the age difference but also the moral and ethical boundaries that society has set. Humbert is in love with a young girl, and this relationship is doomed from the start due to various reasons.
One example is the movie 'Avatar'. The main character, a human, falls in love with an alien - like being from Pandora. Their love is impossible in the sense that they are from different species with different anatomies and cultures, yet they manage to form a deep emotional bond.
Another aspect of impossible love in science fiction is the love between a human and a machine or artificial intelligence. As machines don't have emotions in the traditional sense, this form of love challenges our ideas about what love really is. It forces us to reevaluate the essence of love, whether it's based on physical attraction, emotional connection, or something else entirely.
Another is the love between Heathcliff and Catherine in 'Wuthering Heights'. Their different social classes and Catherine's decision to marry someone else for status made their love impossible. Heathcliff's love turned into a vengeful obsession as a result. Their story is a complex exploration of love that can't be fulfilled.
One common element is external opposition. This could be from society, family, or friends. Another is the internal struggle of the lovers themselves. They might doubt if their love can overcome the difficulties.
One example is the story of Romeo and Juliet. Their families were feuding, which made their love seemingly impossible. Another could be the love between a human and a mermaid in some fictional tales. The differences in their natures and the worlds they belong to create an impossible situation for their love to thrive.