Persona 4 & Atlus' Catherine have done it best as far as I'm concerned -- The former is a platform puzzler that revolves solely around the difficulties of relationships, whereas most games would only go as far as the commencement of a relationship, usually ranging from the hero saving the female damsel from a giant fire-breathing lizard thing or an evil general. But what happens after?
You can argue that the phase beyond probably won't work well in a game, since it would be hard to incorporate into the plot without feeling like a distraction or inconsistent to the overall tone. It's easier to care about a relationship, when it's something you build upon yourself like in the Persona games or BioWare's titles.
I beg to differ though -- Love plays a large part in some of the best games such as Silent Hill 2, where it's not only motivation, it also plays a part in the examination of the main character's psyche -- It's a tragic love story, but a fascinating one that provides plenty of interesting character revelations and growth depending on your playstyle.
Catherine, however, delves into the fundementals from its Persona counterpart, and ask questions in regards to the dilemmas that come with relationships, like marriage, unexpected pregnancies & impetus of commitment. You can get some interesting philosophical obversations from the regular NPCs whom you converse with inside the bar, where large parts of the game takes place, outside the nightmare puzzles. The fact that the game limits itself to this concept so tightly is what makes it work so well, it provides plenty of neat provoking thoughts on the matter when conversing with the characters.
The "romances" in the Persona games work so well, because they feel evolving and authentic, they don't "end" as soon as you complete an arc, they branch out 'till the end of the game. It's mostly thanks to the social link, that manages to provide gameplay-benefits by spending time with your fellow party members. It grants a lot of free-room to get to know them, outside the story, and as a result -- They gain layers. They are also at best not awkwardly written, and tends to focus more on the 'involving lovers' development as people, as opposed to clumsy and silly dialogue. They are also so optional, so even without doing them, the characters can still grow and be inspired by you without being submissive or feel like they've become stock characters and lost all independence. Persona 4 has done it best so far -- It'll be interesting how the social link system will look in Persona 5, and how relationships will function in accordance to the overarching plot.