Ingus and Princess Sara of III (DS). Also, it's suggested that Luneth has feeling for Aria and Refia has feelings for Desch, although these relationships are not defined and not given time to progress.
Cecil and Rosa of IV. Kain of IV also is in love with Rosa, although that love is unrequited. Edge tries constantly to hit on Rydia, but she pushes him away every time.
Locke and Celes of VI have a connection, though whether that is love is both left up to the player's imagination and choices in the game.
Zack Fair and Aerith Gainsborogh of Crisis Core - Final Fantasy VII start a relationship. Their connection carries over to VII proper as Cloud and Aerith feel drawn to each other. Cloud himself already had something of a connection with Tifa, which carries over into Advent Children, although due to Aerith's death, it has a certain tension to it. There is also vague suggestions of a relationship between Yuffie and Vincent.
Love is the central theme of Final Fantasy VIII where Squall and Rinoa's growing relationship is the main plot. Within the background of the game, you find another temporary player character, Laguna, falls in love with a small-town girl named Raine and their marriage is hinted to result in Squall's birth.
Zidane and Garnet of IX fall in love, and it is suggested that Steiner and Beatrix are at least somewhat attracted to each other. Vivi and Quina also get married, but it is not stated whether this develops into a proper relationship. Vivi is seen to have children at the end of the game.
Tidus and Yuna of X fall in love (which is more pronounced in the English version of the game where Yuna openly states it), and the hope of reuniting with Tidus is the main plot point for Yuna in X-2. Wakka and Lulu have a child in X-2 named Vidina, which is the Al-Bhed for future, suggesting that Wakka no longer hates the Al-Bhed.
Although never clearly stated, Balthier and Fran of XII are suggested to be lovers. Fran makes some distant allusions to this in Revenant Wings. Te same situation is true for Vaan and Penelo, although their relationship's potency is a lot more obvious than that of Balthier and Fran. Also, Ashe's husband/fiance was killed in the war between the two empires. She does not fall in love with anyone else for this reason.
Finally, the relationship between Snow and Serah is a major plot point in XIII.
In Final Fantasy Adventure, the relationship between Sumo and Fuji could be called love, especially since he swears to guard her "grave" for the rest of his life.
Bahamut Lagoon has tons of romantic situations. Sendak loves Byuu, who loves Yoyo, who loves Palpaleos, etc. Stuff like that. Of course, the only marriage in the game is between Yoyo and Palpaleos, but that doesn't have a happy ending.
In Final Fantasy Tactics, Ovelia and Delita start to fall in love, but any real FF fan knows how that turned out. And there's a hidden cutscene hinting at a relationship between Agrias and Mustadio.
In Final Fantasy the Spirits Within, Aki and Grey obviously fall in love, and it's implied that Jane and Neil like each other, too.
In Final Fantasy Unlimited, Lisa has and Lou both have a crush on Kaze, but their feelings aren't returned.