My idea of a perfect game differs based on genre.
One of my most desired games would be:
Genre) Turn-Based RPG
Story) A person (age being selectable, along with the character's appearance being customisable) sets off on a journey to travel the Pokemon world and become a Pokemon master.
Art Style) The game would be done in an anime-like cel-shaded style, think Ni No Kuni. Full voice acting would be present throughout the game, all Pokemon would have their cries replaced with their anime voices (though an option to switch back would exist)
Battle System) Battles remain traditional and turn-based as Pokemon games always have been, though they would take place more like in the anime. Trainers taking turn to order attacks, but with the ability to order dodges and counter-attacks. An energy system would also be introduced, so that many hugely powerful attacks could not be used in a row. (If anybody has heard of the Anime Style Battling League over on Serebii, then think like that.) Equipment, as in other RPGs, would also be introduced as clothing for Pokemon, allowing the boosting of their abilities in battle.
Developers) A collaboration between Game Freak, Studio Ghibli and Level 5.
Tone) I would like it to have an Earthbound-esque sarcastically humorous tone. Self-referring characters, breaking of the fourth-wall and such. A few references to Ghibli, Level 5 and other Nintendo properties would also be incredible.
Platform) NX
Controls) Regular Pokemon controls, making use of the traditional gamepad (Analog stick, face buttons, touch screen.)
Length) Main story- ~50 hours, Post game- ~35 hours. Additional content outside of both (side quests, etc.)- ~25 hours at first, expanded later by downloadable content.
Ending) Protagonist saves world from cataclysmic disaster, takes part in the Pokemon League (not the E4, but an actual Pokemon League tournament like in the anime; E4 will instead become the final test of the post-game, headed by the Champion...s. Once the E4 is bested, you are named Champion of the region, following which you are entered into a 6-man tournament against Silver/Kris, Brendan/May, Dawn/Lucas, Hilda/Hilbert and Calem/Serena (which of these pairs show up is completely random- and their teams are different). Once you emerge victorious from this tournament, you fight a final battle against Red to determine whether or not you are a true Pokemon master. (...yes I have given this part of the game a lot of thought :P )
Protagonist) Fully customisable avatar, no longer entirely silent, but rather a character of few words (like the FE my unit.) Rather than a group of personality-less friends like X/Y, you would have a douchebag rival, as in the first two gens, and a more friendly rival, like May/Brendan, both of whom you periodically battle throughout the game.
Antagonist) A league of the members of the defeated enemy teams, united to take over the world. Headed up by Team Rocket's Giovanni, with Cyrus, Ghetsis, etc. as his admins.
End Product) Pokemon NX.