Well. There are many ideas coming up in my head. My most desired game to make would probably be either a Bioware-like RPG or a simple linear story taking place in fedual Japan with a realistic setting. By "realistic" I am reffering to Japanese actually looking like Japanese, speaking as they would speak in that time-period and have the overall cultural tone as accurate as you can have it.
I don't think I've seen anyone having explored this to any extent apart from Shogun: Total War (which doesn't really have a story). It could all take place during the civil wars that raged through the islands between warlords, perhaps at a later time in history when the western world made its influence known to Japan (kind of like The Last Samuraj as insipirational source here), or maybe a "what if" scenario with that the Mongol invasion fleet centuries ago actually succeeded in reaching Japan. In short, many available possibilities that could give the industry a needed refreshment! Bioware did a great job with Jade Empire. I know that game is based more on China then Japan, but my main point is that we seem to focus too much on traditional western settings so that everything else is left in the shadows. No one should have to be afraid taking steps in a new direction!
Also, being the strategy lover that I am, I'd wish for the utimate Science-Fiction strategy game. So far I've seen two types of games in this regard: Those that have all of space at their disposal, but leaves planets as just a piece of background that you conquer to have an increase of resources. Then there are the ones that make beautiful settings on the surface of hundreds of worlds, but leaves space as an observation point at best. Like my wish to have land and sea battles merged together in Total War, why can't planets and space merge in a Total War-like game mechanic?
You would be able to watch and develop your space-faring civilization by building fleets and colonize unexplored areas while also being able to go down to a planet and micro-manage it with for example building cities, putting up surface defences and develop the colony in whatever direction you feel like! And if, for some reason, a battle would occur on the surface you can participate in that should you wish. If you have spaceships at your disposal you could provide orbital support. But of course this would not come without consequences.
If you encounter a planet colonized by your enemy, you could either take the easy way and orbital bombard it which would destroy the enemy base with ease. However this would cause catastrophic impact on the planet's well-being and leave you with a charred wasteland not fit for extensive colonization. Or you could take a more difficult way and invade the planet with conventional armies. This will be alot more tougher, but should you succeed you'd have a prosperous planet at your disposal and be able to reap the rewards for centuries to come! The tactical element to this would be perfect if you ask me, not to mention breath-taking and epic. Come to think of it, this is what Spore has done, although not in the same way as I described.
A game like this would likely be very, very, very difficult and time-consuming to make. Most computers of today wouldn't stand much chance. But the idea is there nonetheless! We'll just have to wait a decade or two... *Grumbles*
Lets see... Was there anything else? Ah, yes! A horror game that makes you feel vunerable! Sure, near 100% of these games can have you die in a cruel manner. But that doesn't mean it manages to have your senses on full alert near constantly. While games like Doom 3 and Dead Space had alot of golden moments, the horror aspect of it was pretty much ruined for me after the first hour or so due to that I could kill seven monsters with relative ease. A true horror game would be, for me, a situation where you have no means to defend yourself with such as weapons or direct force. One game I saw that did this was Clock Tower, where you must constantly run from a crazed madman trying to kill you through an abandoned town. You must be creative, figure out escape routes and hiding places. A game like that would truly make me feel defenceless, and add more to the tension in overall. A simple, yet perhaps among the most effective ways to keep you on the edge is to have an atmosphere of unknown weighing you down without end.
An inspirational source for this could be from the recently-made film adaption of Stephen King's The Mist. All throughout the movie into the very end that uncomfortable feeling in your stomach never makes you relax, through the whole experience you wonder if there will be an end to it, an opening through this fog of doubt and fear. Things like this could add tons of immersion to the experience in a game aswell I'm sure.
...This was a long post. Anyway! That would be the three kinds of games I'd be willing to wait a lifetime for, perhaps even make myself!