FFVIII is the most romantic Final Fantasy, IMHO, and it's so romantic that it's also sappy at times, and occasionally it isn't all that believable, either. However, if you want romantic moments, this one is the way to go. A dance scene, saving the girl (several times), taking a tour around the school with her, going to a concert together, the main character realizing how important the girl is to him when
(SPOILER)she goes into coma, the main character vowing the protect the girl from everyone and be her knight even if the world ends up hating her, hugging, kissing, holding hands... well, you probably got the point already. :D