Well, Spock had T’pring (Amok Time) and the girl on Omicron Ceti Four (This Side of Paradise). McCoy fell in love in “For the World is Hollow and I Have Touched the Sky”, and Scotty was trying to get to know a girl in “Wolf in the Fold”. Chekov had an old girlfriend that showed up in “The Way to Eden”.
The Captain had too many to list, of course, but there were a good number of flings for the others.
Well, Jerry Sohl’s first two drafts (entitled "Power Play, then “The Way of The Spores”) of what became the episode “This Side of Paradise,” had Sulu as the former love interest of Leila Kalomi. D. C. Fontana’s final rewrite had Spock as her old flame.
Chekov was also trying to make time with some yeoman in IIRC “The Apple.” Scotty seemed to be crushing on the lady historian in “Who Mourns for Adonais?” and whats-er-name from “The Lights of Zetar.” Spock fell in love with Mariette Hartley in one of the time travel episodes. Uhura showed some interest in the hot black crewman in “The Man Trap” but of course he turned out to be the salt vampire (who also mimicked one of McCoy’s old flames) and of course there’s Nurse Chapel’s unrequited crush on Spock.