Part of why I love Xenoblade Chronicles so much is that the character interactions were very enjoyable. The main story itself was good enough, showing a good-sized cast of compelling characters that had interesting interactions. However, much of the beauty also comes in all the minor, sometimes hidden, interactions that can be had. Comments made after fights, special comments made during dialogue with NPCs for quests, and the Heart-to-Heart moments all complemented the main interactions very well and made an already great set of characters truly remarkable.
Others that I have to go for are Prince of Persia: The Sands of Time and Mass Effect.
The Sands of Time (and, to lesser extent, The Two Thrones) absolutely nailed the interaction between The Prince and Farah, and I consider it the best single relationship I've seen in a game. Even if that was the only real interaction that occurred, I'd still say it counts.
Mass Effect's characters also largely are what made the franchise stand out to me. They're what brought me back to ME1 when I thought I would never play the game again, and they are what kept ME2's writing interesting even when the overarching story was absolute crap. Even most of my favorite memories from ME3 revolved around concluding the character interactions. Ultimately, even at its worst, the characters of Mass Effect kept me interested, and its best was generally coincided with the best of the character interactions.