When the fans think about Star Trek and romance, they usually remember Captain Kirk. He was the one who had the most relationships in the original series. However, Spock also wasn't entirely lonely. Despite the Vulcan way of life that makes showing emotions undesirable, Spock has had multiple romantic relationships over the years.
Not all of Spock's relationships were as significant and impacted the storyline as much, since his liaisons often failed for various reasons, from death to simply parting ways because the partners weren't compatible or the relationship was one-sided.
T'Pring
T'Pring was Spock's betrothed from the time he was about 7 years old. When he traveled to Vulcan to marry her during the episode Amok Time, T'Pring refused him because she had already found a different partner by then and didn't wish to be Spock's wife.
There was never any love lost between Spock and T'Pring. They barely knew each other and Spock didn't seem disappointed by the fact that T'Pring refused him. Even if they had stayed together somehow, Spock most likely never would have forgiven T'Pring for making him fight his best friend, Captain Kirk, and almost killing him in the process. Their relationship is proof that arranged marriages don't always work in the world of Star Trek.
The Romulan Commander
Spock has never been one for espionage. However, when he and Captain Kirk infiltrated a Romulan ship, Spock took it upon himself to flirt with the Romulan commander. They even touched hands which is an intimate action for the Vulcans.
However, when the commander discovered it was all a ruse, her affection for Spock that had seemed genuine quickly turned to anger and hurt. So while the commander was invested in the potential relationship, it appeared that Spock was only doing his duty and the romance was one-sided.
Christine Chapel
Christine Chapel served as a nurse on the Enterprise and was in love with Spock for a long time. However, Spock never returned the sentiment. Their one-sided relationship made for some awkward moments, such as when Chapel brought food to Spock and he threw her out of his quarters.
The closest they came to having a romance on the original series was when they were forced to kiss by hostile aliens, but nothing came out of it afterward.
Uhura (Star Trek TOS)
In the original series, Uhura flirted with Spock a little and she seemed to have liked him but nothing ever happened between them. What the series succeeded in was creating a friendly dynamic between them instead.
The most notable occasion was when Spock played for Uhura and she sang a song about him and the way he could charm women. Despite the lack of romantic love (from Spock's side), Uhura was one of the people Spock allowed to see his emotions which is rare for Vulcans.
Leila Kalomi
Leila Kalomi is one of the two major romances Spock had in the original Star Trek series. They met during a landing party and Spock fell for Kalomi because of the influence of spores that lowered his emotional control. Just like with other cases, the romance happened under extraordinary circumstances when Spock didn't have full control over himself.
That makes it seem less valid - despite the fact that Spock later admitted his brief relationship with Kalomi was the first time he ever felt truly happy. Even after the spores' influence on him had been broken, Spock still treated Kalomi with a gentleness that hinted at the fact he didn't wish to hurt her even if he no longer could love her.
Uhura (Abrams Universe)
In the rebooted Star Trek films, Spock and Uhura got together in the first film and remained a couple for the subsequent two movies. That presented a significant difference against the original timeline where they were just friends. In the films, Uhura was there for Spock and comforted him when he lost his mother. Nevertheless, their relationship wasn't without difficulties as Uhura got angry at Spock more than once.
The most notable example was when Spock was willing to sacrifice his life in order to protect the Prime Directive. It's unclear where the relationship will move in potential future Star Trek films, whether Uhura and Spock will remain together or part ways. However, many fans aren't so fond of the couple which lowers its overall ranking.
Zarabeth
Spock met Zarabeth in the Star Trek episode All Our Yesterdays when he, Kirk, and McCoy accidentally traveled 5000 years back in time. They got separated and Spock met the young woman Zarabeth who has been living alone in a cave in the Ice Age until then. Spock's behavior reverted to those of Vulcans of this time and he was able to show his emotions freely or had no trouble with eating meat (Vulcans are primarily vegetarians). Most importantly, he and Zarabeth got together but when the time came to leave, Zarabeth remained behind.
They seemed to have liked each other but it's also difficult to overlook Spock wasn't himself when he started his brief romance with Zarabeth. Under normal circumstances, if his mind hadn't reverted back to old ways of thinking, it's doubtful whether anything would happen between them. Nevertheless, their romance had an interesting outcome since Zarabeth had later given birth to Spock's son Zar, which happened in the novel Yesterday's Son.
Saavik
Lieutenant Saavik played a major part in the third, underrated, Star Trek film Search for Spock since she helped the crew bring Spock back from the dead. She also helped young Spock overcome his first Pon Farr, the blood fever that forces Vulcans to find a partner or fight. Their relationship was born out of necessity, rather than love, but judging by Saavik's behavior toward Spock, it suggests that she held a deep respect for him.
However, it later evolved into something deeper as Spock and Saavik got engaged decades later, in 2328, and married even later on. Their respective jobs often kept them apart for long periods of time but they always found their way back to each other and were supportive of each other. All of this makes Saavik one of the most important romances in Spock's life.
Honorable Mention: James T. Kirk
Even though Spock and Kirk didn't have a romance in the traditional meaning of the word, Kirk was the most important person in Spock's life for a long time. When Spock thought he killed Kirk or when Kirk sacrificed his life in the rebooted Star Trek movies, it left Spock deeply distraught.
What's more, Spock thought of Kirk as his t'hy'la, a Vulcan word meaning brother, friend, and lover. And Gene Roddenberry, Star Trek creator, confirmed that Spock and Kirk loved each other, even though it wasn't a physical love. With all these things considered, it's no wonder so many fans shipped the two and wished their romance in Star Trek would have happened.