I became friend with all my companions, but out of all of them, I think that Cassandra, Solas and Sera were the ones my Inquisitor was closest too. Cole was a narrow contender, but I think he came across as more of a little brother that Varric and my Inq looked out for.
Iron Bull and Varric were definitely bros, but I think that while I always listened to them and took their advice, my Inquisitor sometimes felt like a third wheel and out of place due to their already having groups of their friends of their own. Bull has the Chargers with whom he had a long history with, while Varric obviously has the gang from back home in Kirkwall. As Sera notes in her banter with Varric, it makes us feel like we're the lesser cooler group of friends he's stuck with until he can go back to his old gang.
As for Blackwall and Dorian, both are awesome blokes and fun to be around, but the former is a loner and the latter is a tad aloof at times, so it's a tad difficult to see them fall in with the group dynamic at times, which shows in some of their banter.
As for Viv, she's a massive Ice-queen and aside from being a powerful mage, is there anyone who actually gets along with her? Her companion quest was heartbreaking, but it doesn't make up for all the snide and snooty remaks she throws at everyone else. I was expecting for her to be like Morrigan and Miranda and defrost over the course of the game... but that moment never seemed to arrive?