As for a game I would create, I'll go with high realism, newtonian flight model and mostly millitary action, with branching storyline and wingman interactions like Wing Commander.
Something like Falcon 4.0 in space (in terms of gameplay), trying to limit dodgy explainations as much as possible.
In fact, I'd like to see something like that in FSO someday (fully newtonian flight model is almost possible to make already, but AI can't handle it).
Ever heard of Starshatter, Dragon? Heck, Starshatter has several things many of you here would drool over - it had a variable-mode flight model, meaning you could use it like an arcade flight sim like X-Wing or FreeSpace, an in-between mode, and full-Newtonian flight mechanics if you so desire (which I for one, do). Although missions could be scripted, the main driver in the game was a dynamic campaign engine, sort of like Falcon 4.0. The only problem is it's more like "abandonware FreeSpace" than abandonware FreeSpace actually was - you can't buy it any more, and if you're to find a legal copy, it will most likely be used, and furthermore, overpriced.
Now, if I were to design a program, the most influential software to me would be X-Plane in considering its design. The software design would thus need to be modular, albeit efficient, and easily adapted by the end-user to mod to his or her purposes after the fact. A heavy emphasis would be placed upon physics and realism in the software design, so I'd certainly be aiming for a simulator.
The program would need to be released with its own editing tools and software, as well as being able to convert and import data from external programs. And of course, those tools would be easy to use and be fully documented as well.

I'd like to think that the program would be quite reliant on script files in text format - these scripts could easily be parsed by hand or even parsed by the included editing software. I'd like to think that after a time, it would become open source as well.
In the end, I'd probably be going for spaceflight as well in the simulation, even though it's been beaten to death as a concept in this thread already (but then, it's what we like). Thus, you'd have an easy-to-use program like X-Plane in the end with the expansiveness of Orbiter, while simultaneosly, you'd not need to worry about odd set-ups or odd methods of getting something into the program. You'd just as easily be able to fly for leisure as you would as a combatant. Setting up a campaign would boil down to coming up with what ships you'd have to choose from (making an order of battle with ships of given capabilities), coming up with a set of territories, and a set of figures for the involved forces. Think of this as what would happen if you mixed the already mentioned sims with Falcon and Civilization/Master of Orion.
