This'll be a bit long (I'm bored...and at work

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1. Choice to play as a new protagonist, Hawke, or the Warden OR play as one and have the others in your party
I wouldn't mind/care if the Warden remains 'voiceless', but I wouldn't mind him/her being voiced as well (provided it's a good one, I guess. I liked the 'gruff' sounding one for the Male Warden. I think it's NOT the one complaining about a ladder on his back or something all the time...)
Of course, if there could only be 'one choice', I'd like to see the Warden come back, too.
2. Bring back characters from DA:O to DA2: Morrigan, Leliana (and Cassandra), Fluffy the Mabari, Varric, Isabela, Merrill, etc...and have them as companions, with their own quests, of course.
Oh, and more options in terms of what gear they can use (like in DA:O). Or, if they're going to stick w/ the DA2 system, then more options to tweak your companions' gear's looks/capabilities (depending on build, etc.)
3. A longer game with little or no re-used locations (if I go to Noble A's mansion, it'd be weird if has the same interior as the mansion of Noble B and C, especially if the exteriors are different). In the first playthrough, DA2 took me under 70 hours, and DA:O took me under 110 hours.
4. More defining of the scale of the location/s (or 'establishing shots': IMHO, the entry into Kirkwall was lacking in giving the player a sense of the scale/size of the city. A fly-over of the city, like that in the start of Oblivion, would've been welcome. While there is a larger/wider 'shot' of Kirkwall later in the game, IMHO, an earlier one would've been nice)
5. Keep the current combat pace from DA2, but maybe tone down the animations for the rogue a wee bit.

The mechanics, while a bit MMO-ish (esp. when facing bosses), is ok, too.
6. Improvement on visual atmosphere. DA2 is an improvement over DA:O, but it could be better (example: subterranean environments still look a bit 'too bright'. I mean, it's also kinda odd to see torch-lit caverns and then find out that they're infested by Giant Spiders.

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7. Orlais. For the most part, I like the architecture for DA2 (which is why I think it's a pity we aren't given a 'grander view' of it all), and I'm really curious to see how they'd depict Orlais (which I imagine would look less 'bleak' then Kirkwall's environs) and Val Royeaux in particular (especially the main Cathedral thingy of the Chantry)
8. Tevinter. Minrathous, in particular.
9. Par Vollen.
10. An option to see the ENTIRE LINE of dialogue that my character will speak on the dialogue menu (I don't care if they revert it to the DA:O one, or to the radial one in DA2). An option to pick between 'short summary' and 'what I'll say in full' would be nice.
Or a 'mix' of the two: at first display, every dialogue option's like in DA2 now, a short summary, but after hovering the cursor on the option, the full text will display. Something like that.
11. It may not be practical, overall, but I like the idea of my character having a 'backup' weapon he/she can switch to (as w/ DA:O). I'd like to see that back, but, next time around, it'd be nice to see all the carried weapons appear. (kinda like The Witcher, I guess. Sheaths/scabbards would be nice, too

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12. Horses? Griffons? Cthulhu-like sea monstrosities? Mounts!
13. Ship travel. Even if it's just like the travel on the map style thingy in DA:O, but with encounters at sea and 'visits' on various ports.
A full on ship 'mini-game' (think Sid Meier's 'Pirates!') would be great.
14. I was hoping that, for DA2, the whole 'rise to power' thing would involve raising an army. It's not one of the reasons that I'm disappointed w/ DA2, but it would've been nice.
So, an army raising thingy, with options, and maybe some resource management, too, for DA3.
15. I like the Day/Night cycle thing in DA2, but maybe not the 'there's a chest here at night, but not at day (or vice versa)' thing. Night tends to be a bit bright in Kirkwall, too. Still, I'd like to see it return in the next game.
16. DA:O's camera (iso view and detachable camera). It was a pain to fight at times, in DA2, especially in cramped areas or when the characters are near walls or doorways.
17. No more waves...but bigger battles. If there's anything I can say I truly enjoyed in DA2, it's mowing down weak opponents (while running more smoothly than DA:O did with, perhaps, fewer opponents on screen than my typical fight in DA2)...but the 'fun' didn't tend to last long because I had to wait for the 'next wave'.
So, no more waves please...just bigger battles. It would probably be nice to fight in the van of an army, too (kinda like the battle of Denerim...but bigger).
18. More options to affect the storyline. Less 'forced' events. There were some instances in DA2 wherein I was quite annoyed that I wasn't even given the chance to respond to the situation (w/ dialogue, that is). It really felt 'forced'. a
Make me work for an outcome I desire (or something that approximates desired outcome) by giving me options, please (something along the lines of the options available to resolve the situation in Redcliffe and the Arl's son in DA:O).
19. I liked the resource/crafting/enchantment system, so more of that, please, if not an improvement. (maybe have runes that work together well produce additional benefits. Or have the option to mix potions)
20. I don't recall ever seeing Qunari explosives (or cannon) at work in DA2, so I'd like to see that in DA3 (and if Shale returns as a companion, I'd like to mount a cannon on top of her. Or one on each shoulder. My personal warjack)
21. The other good ideas on this thread, like Lulong's and Kilshrek's on this page.
22. Oh, and a game that feels 'less rushed', too.