What companions are the truest friends in the series?

The two (non-romanced) companions that I felt my main protagonists formed a deep connection with were Varric in DA2 and Dorian in DAI. I don't think I can even point out any specific reasons why (although I can say with Dorian that it probably helped that that protagonist did In Hushed Whispers instead of Champions of the Just), but it was just a feeling I got while playing them.

Alistair, Varric, Aveline, Dorian and Cassandra.

For me it`s Alistair, Zevran, Varric (DA2), Aveline and Dorian. I felt they really cared for the PC as a friend instead of just being friendly co-workers. I also think that Morrigan established a deep friendship with the warden in the end but she`s not the most supportive character  .

Overall, Aveline and Varric. The dynamic Hawke can form with those two is outstanding and the three of them have been through so much. Every companion in DA2 can have some great moments of friendship with Hawke though.

In Origins, I actually think it's Sten. You have to earn his respect, but when you do it's truly heartwarming. Oh, and Sigrun - I like her epilogue about how the Warden- Commander spent years finding ways to keep her around instead of letting her go and find her death fighting darkspawn.

I don't feel it quite so strongly with Inquisition, but Cassandra is possibly the closest, although Descent and Jaws of Hakkon make Scout Harding into an unlikely candidate. Who wouldn't want to be friends with a dwarf? They're just so cool.

I actually found Alistair something of a fair weather friend. Even though you stepped up and took the lead when he didn't want to, if you do things he doesn't approve of he is something of a pain, even when you are actually following the suggestion of a senior warden. Also I found him less than supportive of my Cousland PC over his family. Okay so Duncan was his surrogate father but my guy had lost his entire family except for his brother that he still hadn't been able to locate and, if still alive, would be in danger from Howe.

So I do find Zevran and Leliana better friends overall and I also agree that Wynne may seem a busybody but with the best intentions and at least she will admit she was wrong later.

Varric and Averline are the most loyal friends in DA2 but I found that Fenris was pretty good as well even when you make a choice at the end that he normally wouldn't approve of.

I found Dorian the best friend in DAI and I could imagine him continuing to support my female Lavellan over her disastrous romance choice, even though they didn't have him do so in game. It was touching that even though he felt he did need to return to Tevinter, he didn't want to lose touch and so ensured that we didn't with the crystal. I found him an equally good friend to my male Lavellan who didn't romance him.

I also have to admit that Sera ends up a good friend, if you can get over the initial difficulties with her attitude, particularly as an elf. She becomes touchingly supportive by Trespasser, being one of only two characters that actually asks how you are over Solas (if you romanced him) and taking an interest in your clan's safety if they survived or being sympathetic if they didn't. I assume that offering you a place in the Jennies is her way of saying that she wants to stay in touch.

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Zevran and Wynne in DAO. Zev becomes a very loyal friend (and/or lover), when he finally starts to trust you. And Wynne is the down-to earth voice of reason, the warden sometimes needs. She is not afraid to say unpopular things and she can admit, if she is wrong about something, which are both good qualities in a friend.

Varric and Aveline in DA2: no matter what, Varric stays by your side, he might not be happy about some decisions, but he is there for Hawke. Aveline is, like Wynne, a very down-to earth person, who is loyal and tells you the truth, even if you don't want to hear it.

Dorian and again Varric in DAI. Varric is the same loyal friend as in DA2 and Dorian is really good best friend material. I also like Bulls friendship, but since that is connected with how a certain quest turns out, I left it out. Sera can be a good friend too - not so much to a Dalish elf, but to most other inquis.

For Origins & Awakening
I'd say Wynne and Nathaniel Howe
Wynne because she acts like a (grand)mother to the Warden, giving them advise listening to their troubles, that sort of thing
she's made mistakes in her past, and she admits to them, and if you help her come to terms with them she becomes stronger for it
Nathaniel because after all that the Warden did to his home, and his father...he still tries to understand them and gain their trust
playing a human noble, it's also about regaining that trust, not just in him but in his entire family
my current (and one of my favorite origins) Warden is a human noble, she let him go even after he admitted he wanted to kill her
something along the lines of -he's not his father-, because she remembers him for the person he is
when he comes back she's surprised to put it mildly and despite Anders and Oghren disapproving, she allows him to come to reaffirm their friendship (I head canon that he looked out for her when they were kids, and then she had a bit of a puppy crush on him)
and I think that's real friendship right there ^^

For DA 2
Varric, hands down
I mean even if he becomes your rival (which I never have, because my Hawke's tend to be either diplomatic or sarcastic) he will never sell you out to anyone
I mean he could've told Cassandra were Hawke was, but when she asks him where Hawke is because she wants them to lead the Inquisition, he pauses and tells her he doesn't know, even though we later learn he knew exactly where they were, what they were doing and who they were with
Aveline as well, she's a good person and loves Hawke no matter what (err, except if you rival her, which I haven't, but I've seen the vids )
And she's one of the few people genuinely concerned about Hawke (aside from their love interest) when their mother dies

Inquisition...
that's a tough one, I think it depends on my Inquisitors, of which there aren't many yet (I've only played it like...3 times, and I've yet to finish the dlc's)
but I think Cassandra and Dorian are good friends of my Quizzies
with Dorian they can gush over cute men, and with Cassandra about their love for books, maybe the three of them can even start a book club, invite Solas every so often (he seems type to like that sort of thing xD) ^^
though with Cassandra they'd have a few points on which they'd butt heads, and that's religion
as an atheist myself, my canon Inquisitor is one as well, sure she was raised as an Andrastian, but she believes that if the Maker really cared he'd just show up and knock some sense into the world. But other than that, yeah...Cassandra would be a great friend of my Quizzy ^^
Or, hm...maybe Cole? He's a helper, and he's a good person/spirit ^^

This is simply not right. He protects Hawke, but tells to Hawke, the Inquisition needs him/her.  If Hawke helped the mages to escape, NO reason to Varric to trust in a Seeker, who kidnapped and interrogated him. Probably supposed, this fate waits for Hawke too. You know, an interrogation not a five o'clock tea. Cassandra is a Seeker. A mage hunter. No reason to trust her.
If Hawke supported the mad woman, probably Varric still thinks, Hawke needs some rest.

The friendship is selfish. Just like everything. Yes, we can say. Everything that you do for people you do for yourself as well. What your problem with Varric? He's absolutely okay. Varric's not a saint – a killer, like everyone else in the game. But a very good friend.

Or Anders is the ONLY altruist in the whole game... You agree, you not?

I don't want an essay – but a reason, why a bad friend is Varric. He keeps Hawke's secret but informs Hawke. When Cassandra kidnapped him, probably wouldn't able to speak Hawke – so he waited the moment when he able to inform Hawke, without betraying him/her.
Yes, betrayal. Regardless, Hawke wanted to help, Cassandra still a Seeker, who interrogated Varric. You know, what it means? 

Cole's not altruist – he's a spirit. Spirit of Compassion. Comforting/helping the suffering people is his essence... He only can be an altruist, if he become more human.

And I didn't say Anders altruist, because of the mage freedom – but of course: he able to sacrifice everything for it – even his friendship/love with Hawke. And he was already free (and possible he lived in the Hightown in love...) But I spoke about the Darktown's free healer.