The Primrose Path
Kain has one love interest the entire game, and that is Rosa Farrell. Unfourtunately for him, Rosa loves Cecil. This proves troublesome.
According to various official sources, Kain and Rosa were dating before she realized her feelings for Cecil. He's not just some crazed stalker, he cares for Rosa deeply. And she cared for him too, but she moved on. Kain just hasn't.
Nobody wants to be left for their best friend. It's a painful thing, because not only are you left, but you can't let your anger show, or else you'll lose something else. Cecil and Rosa are reluctant to show their love at the beginning of the game, perhaps because they don't want to hurt Kain. But Kain knows what's going on, and he doesn't say anything.
His love for Rosa is demonstrated even when he is being controlled by Golbez, although his desire to prove himself superior to Cecil seems to be his driving motiation. Rosa, like Cecil, maintains faith in Kain through the whole affair, when others are much more willing to distrust him. However, Kain's betrayal certainly led her closer to Cecil, despite the fact that Kain wiped the floor with him on one occasion.
It's unknown exactly why he loves Rosa. My guess is that he admires her beauty and kindness. But enough is enough, and this admiration turns into a bit of an obsession -- one that generates some unspoken resentment towards Cecil. When he is controlled by Golbez, this resentment is no longer unspoken, and Kain's feelings become a bit obvious. Once he's back to his usual self, Rosa manages the situation nicely, telling him that he'll always be her friend, even though he had turned against them. After all, it wasn't his fault. Rosa and Cecil never discuss Kain's love for Rosa, and I think they choose to ignore it because they know that discussing it would only hurt Kain and create more tension.
At the end of the game, it's unclear whether or not Kain still loves Rosa, but my guess is that he still does. He's extremely upset for letting her down, and he feels the need to change for her, in addition to changing for his best friend and father. He also doesn't show up to the wedding, convincing himself that it is because he has let his friends down. While I think he means that, I also think it would hurt him too much to see them being bound together eternally. Whether or not this is the case, we do know that Rosa is still very important to him -- it's up to you to decided whether it's as a friend or as something more.
It's also quite clear by the end of the game that Kain will never be with Rosa, barring Cecil's untimely death, and Kain's trying to stay away from that grisly route. Kain will probably try to move on. It's easier said than done, but he knows what it is to let a dark longing devour your very soul.