Damn, I get back from work and there's a ton of stuff to read...
In regard to story / gameplay, the two don't have to be mutually exclusive, and in fact every single game ever made already has a story even if there's not one scripted into the game. Most games today actually have two stories going on:
1) The story that the developers wrote up and added dialogue and cutscenes for
2) The one that describes your own personal experience with the game, written as you play.
Story #2 is almost always going to be the more compelling story for a player, and it's usually the one you talk about, even if the game involved has an amazing story written into it.
The sad fact is that a lot of games now sacrifice Story #2 for the sake of making Story #1 feel more... epic? Cinematic?
Since my Skyrim cred has been called into question, I shall use it as an example:
Remember the first dragon you fight? The one outside Whiterun? That dragon made me rage-quit that game and I almost uninstalled it and never played it again. That dragon was the most disappointing gameplay experience I've had since the opening driving sequence of GTA4 (which I also rage-quit after...)
So I'm level 6 or 7 or something. I've done a couple of easy fetch-quests so far just getting used to all the ins and outs of everything and then I goto Whiterun and there's a dude there and he's all "Holy shit! There's a fuckin dragon flyin around!" and the king guy is all "Fuckin go out there and help my dudes check out this dragon!" so I go out to meet up with the dudes where the arrow's pointing.
So I get there and this chick is all "be vewwy quiet... we're hunting dwagons... hehehehe" and we go to this watch tower that's seen better days, and this dragon flies over and the dudes are all "fuckin DRAGON!"
At this point in the game, I had an axe and a bow and about 20 arrows and a couple health potions and my armor was crap. I'm level 6 or 7. I firmly believe that this is some kind of scripted bullshit because there's no way I'm about to fight a fucking dragon this early in the game. There's just no fucking way.
The dragon lands and starts flinging guys left and right and takes off and breathes fire and lands and flings some guys. I shoot some arrows at it and it gets hurt. I shoot some more arrows at it and it gets more hurt. It lands and I run up to it and wave my axe at it and it's all "OW! FIREBREATH!" and I get mildly scalded. So I back off a little and then shoot more arrows at it and it dies. I absorb it's soul and all the dudes are like "holy shit, bro, you just ate that dragon's soul!"
And I hit ESC, save the game, quit the game go outside and smoke several cigarettes while trying to keep myself from punching things at random, so pissed off am I.
Now, I had already kinda had my doubts about the game after having wrestled a bear to death at level 2 or 3, but taking out a dragon at lvl 7 with a bow was not exactly what I had imagined going in. I had envisioned a game where the dragons were a thing. Not just some random enemy they would throw at you nonstop for the duration of the game, but something special that you'd get to fight maybe a half dozen times during the main quest and maybe every great once in a while otherwise. They would have been huge and varied and important. If you saw a dragon and you weren't at LEAST lvl 30 or 40 and decked out with some decent gear you would stand no chance. A dragon encounter would mean running like a bitch for someplace to hide until the big scary monster went away.
But while I was outside I basically had to tell myself that OF COURSE that's what the game was. I had to force myself to lower my expectations down to nearly nothing at all because these guys were trying to give me a visceral experience. It doesn't matter that you shouldn't be able to kill a dragon at lvl 7 with the weakest bow and nearly the worst armor in the game. Games don't give a flying fuck about that. Skyrim is a simple power fantasy. You're the star of your own epic fantasy adventure.
Dorkman pointed out that having fun and being told a story aren't mutually exclusive, but it depends on what your idea of 'fun' is, and what your idea of 'story' is. Those two things are pretty well defined for us in movie terms. You've got movies that are all about 'fun' like Star Wars and ID4 and 2012 and Transformers, and then you've got movies that are all about story like Schindler's List, The Prestige and The Fountain, but then you've got movies that try to do both as well as possible, or are some decent mixture of both, at least.
With games, I think those two things are a bit more nebulous. Fun, especially, is extremely subjective. I tend to play very strategic, very micro-management oriented games. Not as much now, maybe, but back in the day I was all over some of that shit. The Ultima games, oldschool adventure games where you had to keep your own notes of what the hell was going on, tactical war sims (I never found a copy of The Operational Art Of War, but I fucking want it badly), and today I play Dwarf Fortress and other roguelikes / RPG's that require a lot of detail awareness. A lot of people would find that sort of thing extremely boring.
On the other hand, many people obviously find more visceral games fun and I usually don't get off on that sort of thing. Sometimes the physics can be good for a laugh. The physics and ragdolls in GTA4, for instance, is the only saving grace for that game for me. Literally every single other thing about that game makes me angry. The only thing I ever do in GTA4 is perform random acts of cruelty and generally incite chaos. It is the only thing in there that I find fun at all.
When you're talking about story, again, there's a story going on in games that have no story. In Dwarf Fortress, which is the game I play most often lately, there's no story being told to you. The story is what you do with the game. Your goal is to just make and expand a Dwarf Fortress (I know, hard to imagine...) and keep it going for as long as possible. However, you only have the ability to tell your dwarves what you'd like them to do. It's up to the dwarves whether or not they'll actually do it. You're more managing a workforce than controlling characters.
Each dwarf has a personality, favorite foods, favorite colors, friends, enemies, personality quirks, job preferences, physical descriptions, etc. If one dwarf dies, all of his friends will mourn him and it will affect their willingness to work, sleep, eat, etc. It is one of the most detailed, challenging and rewarding games I've ever played, and the stories it has generated have been amazing. They aren't the sort of stories that have beginnings, middles and endings, but more shit you can talk about to other people who play the game who may have had something kinda similar happen to them, but usually not that specific thing...
Hard to explain... here's a couple examples...
http://dwarffortresswiki.org/index.php/Bronzemurder
http://www.timdenee.com/oilfurnace/
That's the sort of story I dig on in a game. The one you make up as you go.
If you were to take Dwarf Fortress and try to give it a storyline with like... quests and missions and specific characters and plot moments and stuff, you'd have to start ripping out the mechanics to prevent the players from doing things you didn't want them to do. The main characters couldn't die cause you need them for the story. You'd need an overall goal, so build this and this and that and then 30 missions later you get to the final mission which is to have your dwarf militia defeat the big boss creature and his army of zombie hamsters.
And then it's the same story for every person who plays it. You now play Dwarf Fortress once or twice and then never again, because you've already played it.
The one thing I do in Skyrim is run around and explore. If the game were built in such a way that me doing that was THE POINT of the game, and the game were generating content or doing something that would provide me with a unique experience every time I played it, I would play it a hell of a lot. You could play it all the time and so long as the mechanics were FUN for you, you'd be making up your own story as you went along and enjoy it.
A perfect game, in my opinion, is one that can combine a set of rules and mechanics with the imagination of the player. Adventure games are awesome and telling stories is awesome, but that isn't the natural form of the medium. That's not what it's good at doing. If you want to tell a story, there are tons of non-interactive mediums to choose from.
I'm glad the discussion has become more general and not game-specific (I guess I ruined that again...). Originally I wasn't trying to pick on ME3, I was just using it as a springboard into a discussion about story in games, or maybe just games in general and my overall dismay at my own perception of the medium as it currently stands. I've never played ME3 and it's probably better than I assume it is, and from what I've seen, it does at least use that interactive ability in ways that alter the story that the devs are trying to tell. Though, honestly, I'm not sure if that's a good idea or not either, just on a basic storytelling level.
That might be something else to consider, tho. How much outside input can or should a creator allow to influence his story before the point of the story is lost or weakened or whatever?