In my Eb Maclean books, Fortress of Lies and Judgment Tramp, the protagonist wants love but has an underlying fear, because of his past, that he may be unworthy of it. He is "damaged goods". His desire to love again and fear of remaining distant from it, is a driving force behind solving the books' central mysteries and peeling back the layers of deceit within his own family. Eb's trust and anger issues, as well as his (not necessarily ungrounded) paranoia further complicate things. His two sisters keep secrets from him, and he often finds himself in danger because of them.
A protagonist's love life can serve a useful purpose within the story framework--and more than that, it can be a foundation for every other aspect of the story. Janet Evanovich uses the two men in Stephanie Plum's life to give her access into a shady world that she would otherwise never experience. Ranger is her mentor, helping her to learn and survive as a bounty hunter, and Ranger's business interests also provide an almost endless number of mysteries for her to solve. Stephanie's other love, Joe Morelli, is a cop. It's natural that Ranger and Joe Morelli will tangle with each other occasionally, just as it is also natural that they will occasionally come together to help Stephanie when she's gotten herself in too deep. The other loves in Stephanie's life, her worry-wart mother, her long suffering father, her eccentric grandmother, all contribute to the chaos. The end result of those complex (and oftentimes comical) relationships is a fiction writer's dream.
Relationships always come with baggage of some type or another, and that can help us make sense of why a character does certain things--and often the key relationship in someone's life provides the impetus to drive a character to risk everything to solve a mystery. Eb Maclean isn't looking for trouble, but when someone puts a bomb in his sister's car he is forced to find them--because his sister, Maggie, won't be safe until that person is caught. Eb's deep love for Maggie is revealed when the reader sees what lengths he will go to in order to catch the bomber, and the possible consequence of losing her raises the stakes of the game--to a point where Eb must solve the mystery or lose everything that he cares about.
Love can also allow us to see a softer side of a character--and at the same time reveal what humans are capable of doing for love. A person can commit a crime for an altruistic reason--a man could rob a bank to get money for an operation that might save his son, and it could spiral out of control from there as the situation turns into a hostage crisis inside the bank. Is the man a good guy who made a bad choice--or is he a bad guy with a good motive for this one particular crime? The story could be written several different ways, but the love for his son would tend to humanize the man in the reader's eyes in any case.
There are many ways that a protagonists' love life can mold a story--and working the relationship angle to the fullest can make the difference between a flat, lifeless story and a great read. Love has everything to do with it--because it is a big reason why people do what they do.
How does your protagonist's love life impact the plot of your work?