Okay. So suppose you have the opportunity to make any sort of videogame you like. Budget is not an issue. Technological limitations are not an issue. The tastes of the gaming public are not an issue. It can be as wildly impractical and unmarketable as you like--it just has to be the sort of game you dream of playing.
What do you end up making?
Note: The description that follows ended up much longer than I expected. Feel free to skip it and get to your own dream-game creation.
Here's one that I've been dwelling on for some time now: Untitled FIrst-Person Chase Scene Game. The game starts out with minimal exposition--you're in an alley, meeting a shady-looking contact who hands you a briefcase and explains that you need to get it to a certain individual at a certain building across town (no explanation is given at any point in the game). Then, shortly after he makes the handoff, some menacing MIB types show up and charge after you. Unarmed, your only option is to run like hell.
Running is the name of the game. You won't pick up any weapons, and your hand-to-hand combat skills are unimpressive. You can try to fight off your pursuers, but you won't last more than a few seconds. All you can do is try to escape as you make your way to your target (which, conveniently, is the tallest building in the city and has its name emblazoned prominently across it). The running/jumping/sliding/etc. mechanics are much like those in Mirror's Edge, although you aren't quite as agile. You won't be pulling off fancy parkour maneuvers, but you're definitely a better-than-average runner.
The entire city is open to you. Every building is fully modeled, exterior and interior, with realistic physics for every object. You can duck into any building to try and elude your pursuers. Push over bookcases to block doors, pull a fire alarm to cause a crowd to panic and provide convenient cover, swipe a hat/jacket from a coatrack at the entrance to a restaurant to use as a makeshift disguise, etc. Stealth is sometimes an option, but you'll eventually get spotted and have to get back to running. The game gives you plenty of options for eluding your pursuers, but no place is safe for long--if you don't keep moving, you will get caught.
You don't get any sort of HUD or map, but because your destination is clearly visible from most locations in the city, you're unlikely to get lost (the city is big, by the way--a straight shot from the starting point to the target building would take an hour, and you're probably not going to have much luck taking that route). As you elude capture for longer and longer, the search effort intensifies; you face more and better-trained agents. They'll call local law enforcement on you (or, if you're a bit too destructive in your trek through the city, you'll catch their attention on your own). Eventually, they'll stop trying to take you alive and instead open fire whenever they get a glimpse of you. Then come the helicopters and snipers.
If you make it, you still have to make your way up the building. Which is, of course, on full alert, so stealth becomes crucial. When you finally make the handoff, the ending you get depends on your completion time, a la Metroid. The game's short (a couple of hours per playthrough), but it's designed for speedrunning, and the paths through it are virtually unlimited.
So that's my impractical dream game of the moment. What's yours?

I have 2 of those, actually.
First of all: Fragile Allegiance 2 - like
For people who do not know FA, it's like Master of Orion in real-time, which makes it my favorite. And what would I want? A 4X game and an FPS in one package. That means a huge strategy with lots of choices and variants, where AI is advanced enough to run an 'empire' on it's own. When the game starts, you pick what you want to be - a soldier, a captain, or a president or whatever. That means you could play trough a 4X game from a perspective of a lowly squad member used in front lines, as well as captain of a huge battlecruiser or the guy who leads it all. Campaign would be something like advancing trough ranks to the highest possible one.
Aaand the second one:
Apocalypse survivor game. All people in the city you live in disappear and you're on your own to survive. That means a whole accessible city you're free to explore, hand-made to the last room of the last apartment building. You would be just an average Joe, so you'd probly start by robbing shops and another appartements, probably continue by hunting animals... Game would get harder as running water would run out, electric grid would go down because no one's taking care of it etc., and when everything gets worse and worse, you'd find another survivor - and another part of the game would be basically about trying not to kill each other. You would get to slowly uncover what happened, and revert it ... maybe.

I always wondered if you could make a Star Wars type of game, but have all the different game types available during a campaign (although you could pick which ones you'd like to do).
For example, you begin with a 4X space view, you might have a fleet battle (which you can play either commanding the fleet or piloting a ship yourself), then you might attack a planet (RTS bit here, or perhaps jump into a vehicle?).
Obviously for special missions you should also have the opportunity to take control of spies or jedi or whatever (FPS/TPS).
Or alternatively, you could let the computer do the work and stick to the 4X part. How much you want to personally oversee would be your decision. If you failed a mission (say a spying one), it wouldn't be the end of the game, just a setback.
It truly would be a grand strategy game.

let's make a game, shall we?
(damn mind reader! :D )

Impractical huh? Well, DRM free without GFWL or Steam in the background. That's impossible for 90% of the market already.
Add in gameplay that lasts for years with skirmish type modes that can be played co-op, alone, online, LAN, and no need for serial checks to do so. That way you can install the game you own for your little brother and play with him. Add that in and you cut out 95% of the total game market.
Add in good gameplay that makes you leave with a smile on your face every time you play on top of the above conditions. That leaves out 100% of the game market, hence an impractical dream game.

Heh, yeah, I thought that would be neat as well. But describing every detail of it would fill up a whole damn screen, that applies to the game I have described above it as well :D I can see why it would not only be hard to do, but maybe even un-doable. And that's evil.

If only I had the money or the skill, I'd totally take you up on that offer!
It would be a cult classic rather than best-seller I feel. I'd like to think it would have a legion of highly obsessed fan modders.
Your second game reminds me of Robinsons Requiem. Kind of a survivor type of game, except it's set on an alien world or something. That, but mixed with zombies and in an urban setting. I guess that would be how I'd have liked to see Fallout 3 play out.
[edit] seems I'm not typing fast enough, ninja'd on my Requiem comparison!

I'd make Dungeon Keeper 3 ;-)

I think the perhaps one of the best solutions to actually play a game like that is to throw the 3d out and use simple graphics (like Geneforge say).
If the game still had amazing depth i would fall deeply, madly and forever in love with it.
Gimme a real sandbox where i am rewarded for creative thinking or even just being the first to grab the yellow pages and find the local gunstore before the npc's loot the place.
I would happily play till dawn whilst getting pissed on cider and worrying it the old newspapers i collected are really gonna keep my character warm enough in the upcoming winter months....Ahh gaming nirvana.

Duke Nukem Forever

As much as I love Fallout, this sounds like what Fallout should have been.
Another one: Some sort of game where you only have one enemy. A foe so overwhelmingly powerful that you simply can't face it head on for long (you can scrounge up assorted weaponry from the bodies of those who tried to take it down before, but they don't have much effect). Let's set it in some underground, Black Mesa-y facility. You have to avoid detection and observe the monstrosity from the shadows, learning its behavior patterns, trying to figure out its weaknesses. Guide it into traps, chip away at its armor bit by bit, and ultimately prove yourself the superior hunter.
(I guess some of the hunts in Monster Hunter are something like this, but this should be much grander, with the potential for gratuitously explosive set pieces.)

Oh thats nearly practical, come on reach higher.
How about each of the elements you describe is a seperate game with its own story driven campaign but are capable of being linked for an enormous multiplayer campaign? The game would normally simulate the decisions and outcomes of areas outside your sphere of influence and give you a generic single player campaign but when linked the games stop simulating and human control determines the outcome of other segments.
The objective is to secure the planet Thyferra to ensure imperial control of bacta.
The fleet admiral player uses the homeworld style game to jump his fleet into the system, take up a position and begin to engage the rebel fleet whereupon he deploys his TIEs to gain space superiority and perform precision strikes on enemy cruisers
The TIE Fighter player uses the sim game which begins his mission at the same place where the fleet admiral launches and he gets his mission objectives from the admiral so its essential to the war effort than the starfighter player does his job. The admiral would issue an order to escort a transport through a gap in the planetary shield so the ground forces can take the shield generators
The special forces team is deployed by shuttle and commences the mission using the stealthy third person shooter game. He advances through the countryside using cover and quick kills where possible to minimise resistance when taking the shield generator. When the generator is taken, the shields are lowered for either bombardment or ground assault
The fleet admiral makes the call to capture the world intact to minimise infrastructure damage and deploys his bulk landing craft to deliver the imperial army to the planet and orders the fighters to provide cover if there are still rebel forces in the area (I'm thinking they jump in a few flights of xwings & ywings for harassment attacks after the rebel fleet falls)
The fighter pilot runs escort for the bulk landers and defends the fleet from the rebel harassment strikes, depending on how successful the fighter pilot is, the amount of resources available to the ground troops may be diminished
Once the landers have unloaded, the ground assault player takes control with the Operation Flashpoint style game, assuming command of a stormtrooper sqaud, AT-ST scout or front line AT-AT depending on the role they fancy playing, advancing as an all conqering army taking out rebel and native resistance forces and capturing strategically important locations on their way to make a grand show of strength at the planetary capital.
If the ground assault team have trouble with a strong defensive position, they can issue a request for support and the fleet admiral would make the call on who to assign to the job. If the target is in an out of the way location and the fleet is in a good position, they can bombard it with turbolaser fire until its nothing but a puddle. If the fleet isn't in a good position or if the target is close to an important capture objective, the admiral could detail a fighter squadron for a precision strafing run (becoming a bit rogue squadron for the fighter player). If the target is something that could be turned to Imperial use, the admiral could assign the special forces team to move in and capture the target, turning the enemy weapons against them
Once the rebel fleet have been routed and the ground forces reach their firing position on the governmental capital, the planet would surrender to Imperial control and the first of many missions would be complete.
Now THAT'S impractical! Also awesome

My inner Star Wars geek is salivating.

My impractical dream game would be like dead rising, only bigger and with a management thing: you could get hungry, you'd have to sleep so you have to find someplace to sleep safely (you can barricade doors et al), you can have safe-houses, ...