Not sure if anyone suggested this before, but I think it would be cool to have a Tranquil companion. During the Mage-Templar war, he/she could have escaped one of the Circle towers and been taken in by a band of mercenaries, learning to fight as a Rogue. Being devoid of emotions, he/she would be very stoic, practical to a fault, following orders without question. Then, the story could offer an opportunity to cure his/her Tranquil state, a choice that would be influenced by the protagonist. If cured, the companion would regain his/her magical abilities along with his/her emotions, paving the road to a completely new character, and even a potential romance option. The ex-Tranquil could then integrate his/her magical abilities with his newly acquired fighting skills, making a mage-rogue combo class being able to throw winter grasp infused daggers, opening locks with his/her mind, and why not even conjure some sort of "healing arrows" made entirely of magic which he/she could shoot at other companions ?
And how about another companion immune to the Darkspawn taint ? The story could take you to an area recently defiled by Darkspawn, in which you'd find a lone survivor (Warrior class) fighting off Ghouls. Throughout the course of the game, you'd get to learn more about his/her past of fighting Darkspawn without being a Grey Warden and the mystery surrounding his/her immunity, along with a possible tie linking him/her to Andraste.
I'd also like to see the Hero of Ferelden back in the game, either as a cameo or a guest companion along with the First Warden, leader of the organization which we have never seen as of yet. Also, I think Valta, a character from the Descent DLC, could be an interesting companion considering what happens to her in the DLC (no spoilers).
Oh, and instead of a Mabari, why not a Griffon animal companion ? Supposedly, there's a Dragon age novel in which the characters find Griffon eggs in the modern Dragon age world.
I'm for basically all of that.

Sounds good.
Alright, for my wishlist:
1. Programmable tactics returned and improved.
2. Complete sidequest overhaul, W3/DA:O style.
3. Not anywhere near so much empty space. Yes keep the wide open feel in some areas, but mix it up and fill those areas chock full with quality content. Like has been said 1,000 times, quality over quantity.
4. Tight pacing. Story should flow strongly throughout. No more gating the story behind busy work accumulation. No more lifeless busy work.
5. Origin stories!!! And continue with race selection, etc.
6. More serious tone. Joke items and the occasional codex joke, lighter moments, that's all good. Keep that, but the rest of the game should strike a serious tone, have weight and consequence and feel dangerous. (No real occult crap though. ... Don't let that keep creeping in, don't spring that. That's the only problem I have with W3, and a ton of other otherwise quality stuff out there now.) Keep it dramatic, but keep it RW clean. Same thing goes for social agendas, keep it consistent with the fiction, in that context.
7. Romance was great! Companion interaction hit a new high overall. Mostly don't restrict any of them to pg13 content like it was for some this time, but that's the strongest area of your games by far. So, just more of the good stuff.
8. Sera. I want to see her mystery continue to unfold. And I just like her.

She'd be awesome in a slave uprising scenario.
9. Warden, Morrigan, and son cameo. Because you missed the boat this time, and that sucked. Morrigan should have more to do here.
10. Merrill, Fenris, Charade, etc. Characters whose appearance makes total sense.
11. New protag with new playable origins.
12. 80% - 90% new companions, excepting returning minor characters like a Finn or a Dagna, etc. No Varric or anybody else that doesn't make sense.
13. Major branching main story, some branching in every side quest for that matter. Choice and consequence we can actually see to whatever extent.
14. Better presentation, cinematic dialogue, more actual cinematics in general, interactive by the wheel and all.
15. Wider range of customization options, from stats to armor to home base to character body build, it's full next gen now.
16. Better hair, long hair, at least simple hair physics, breast physics, more natural skin movement, weapon sheathes and stocks, all sorts of little things like that. Full next gen now. ME3 last gen still looked better, as pretty as the environments could be in DA:I. Procedural and contextual animation. Synched combat movement with visible automatic defense (improve on DA:O/KoTOR style) and things like that. Finishing moves. More immersive and impressive animation systems. Don't waste so much dev time on big superfluous filler stuff.
17. DLC that maintains a certain level of ambition and a high quality consistent with the best parts of the base game. Otherwise, don't charge so much. First two dlcs felt like price gouging.
18. Mounted combat, with its own hp (or guard, whatever), combat skills, etc. And the companions don't disappear.
19. Consistent banter and music. Contributed to the empty feeling.
20. Tavern songs. :-) I loved them. I'd love for a companion to have that role.
21. Keep utilizing the Dragon Age Keep.
Alright, think that covers it.
Editing: All done. :-)
Edit 2: Keep on Keeping on.