For me it's a close call between Cole/Cassandra and Cole/Solas. It is touching and a demonstration of the integrity behind Cassandra's hardarse duty-mindedness to watch her attitude change from "SKEWER THE DEMON!" to almost sisterly affection. Cole, of course, is kind to everyone, but I had the impression that he puts in special effort to earn Cassandra's trust. Since he is my all-time favourite Bioware character and she is not far behind, I was overjoyed when they started to bond with each other. Bonus "Aw!" points for the two times he refers to the two of them as "Faith and Compassion" -- it's like Cassandra gets to be an honorary spirit.
The only thing that sours this friendship is the immersion-breaking oversight of it not being reflected anywhere outside their banters. Same with her cautious curiosity about the Fade and even concern for its creatures shown in a few banters with Solas, which is another interesting and surprising positive relationship that I enjoy a lot.
Solas' bond with Cole on the other hand is, of course, entirely unsurprising and utterly wonderful for its mutual affection, respect and unique understanding, as well as the wistful mysticism and insight in their talks about the Fade and spirits. That is pure poetry, I could listen to them for hours.
Together, these three are definitely the highlight of the game and far and wide my preferred party combination.
Honorary mentions to Cole's interactions with Dorian and Blackwall (especially more-spirit Cole and post-Revelations Blackwall) for the very well-done combination of touching, thoughtful and unintentionally humorous moments. Looking back at the Cole/Blackwall banters provides so many clues about Blackwall's big secret. For example, the time he asks if Blackwall's beard is a mask? Turns out it is, because Rainier grew it to make himself look more like the real Blackwall. And as for Dorian, Cole is the one companion that I felt Dorian allows himself to be open and vulnerable with, at times. He so badly needs people around whom he doesn't feel he has to hide behind bluster or humor.
For a mostly light-hearted and humorous change of pace from all this deeper stuff, Dorian and Varric are a great combination. Gotta love their outrageous bets and banters.
Dorian: You said we'd be ass-deep in trouble. This is more like knee-high.
Varric: I didn't specify whose ass, did I?