My ideal games, by type:
FPS:
FEAR came close, but I'd rather be a wizard and occasionally go invisible, control minds, or just destroy large groups with withering fire.
RPG:
Grand scale - Something with a unique and fascinating setting or backstory like Morrowind, but rather than just running errands you, if you want, lead armies, or assassinate kings.
Speaking of assassinate kings...
Story-focused - As a mass market release, it'd be hard to beat the Witcher. The "Full Combat Rebalance" mods take it that step further. Into something even grittier and more challenging.
And speaking of gritty and challenging.
Small scale - STALKER, with a bunch of mods, fits the bill well. Explore, kill things, gather anomalies, have the occasional conversation over some rotgut, camp, run away when you hear something you can't identify. Hard to beat.
Strategy -
4X: Civ, highly moddable, with a much much better AI would be great. Fantasy or sci-fi for bonus points. (So ... FFH2, with a better AI.)
Tactical-RPG: I'd like a faithful, but updated, version of Jagged Alliance, please. X-Com, and Fallout Tactics were pretty good, too. Something with some depth.
Tactical wargame: "Combat Mission" with an overhauled AI, better graphics (why not?) and TCPIP wego is what I dream of.
Casual wargame: Games like Panzer General and its clones or Battle of Wesnoth are a not-quite guilty pleasure.
"Real" wargame: Anything with a campaign. Just give it graphics that make me glad I bought a computer this century and a good AI.
Flight Sim
IL2 + mods, installing from a single disk, all at once, with custom hardware.
Board games:
It exists, but I currently dream of Illuminati, with the cheating rules, so ... it.
Traditional games:
Go, but changed in the only way that could possibly make it better: Added laser beams and explosions. But
is it possible?
CCG/LCG:
L5R with rules as simple and elegant as Android Netrunner.
Or Android Netrunner, with cards that are better templated, ala MTG.
Or MTG, with all the cards burning in hell.
Any of those would be great.
Pen & Paper RPG
I like having different games for different genres ("realistic" being a genre in this case, for which I use GURPS. (Hi, Gori!)), but my favorite is Ars Magica. My dream game would be Ars updated into the modern world, but with slicker, somewhat more sophisticated rules. (ie, what Mage should have been

!)