My ideal game would allow you to travel to all five regions, allow you to run into wild pokemon (perhaps even seeing them in the grass before they attack), open up all 32 gyms (although they would not be part of the MAIN plot), encounter shadow pokemon, and generally just have a deeper plot than any of the previous RPGs had to offer...
FOR INSTANCE:
The game starts off in Orre where, unsurprisingly, Team Snaggem's base explodes (again). This time, a mammoth pokemon bursts through the roof and flies up to block the sun. The pokemon doubles back and reveals itself to be a giant purple Latios/Latias-type pokemon. It flies down and picks up two of the Team Snaggem members fleeing from the explosion, lifts them into the air, and drops them from an unsurvivable height. After that, it flies away.
Miles away, a big black truck pulls up in front of a ten year old kid's house. The child is playing with their Eevee in the front yard when several men suddenly burst out of the truck and attack the child. The kid's mother runs outside and unleashes her own pokemon, a high-levelled Elekible, at the newcomers. A double battle then starts (the child is your character, you pick the gender. For the rest of this, we will assume it is a boy.). The attackers are Team Snaggem and they have come because your father "ratted them out" and they want to make him pay. Luckilly, your mom's Elekible drives them back, but not before they manage to snatch your Eevee and run. After the fight, you and your mom move away from Orre. (Your father was a police officer who infultrated Snaggem. Something went wrong... and he turned on them, detonating the base. Snaggem makes no mention of whether he survived the blast or not.)
Five years later, you decide to go back to Orre and find out what happened to your father. You leave one night, without telling your mom, and get on a boat destined for Orre. On the way, you encounter a lost Houndour puppy that follows you and takes a liking to you. You catch it, providing you with your first pokemon for the game (that insists on being out of its pokeball).
You progress through Orre (which now has a good amount of wild pokemon, not just in those four spots, but they're still pretty uncommon). You discover Snaggem is STILL active in the area and you find their fortress in the desert. You break in and stop their novice plan to simply close the hearts of pokemon. In the fortress you run into your Eevee again and it is so happy to see you that it actually evolves into either Umbreon or Espeon, depending on the time of day you attack the fortress. Your Eevee and Houndour cannot be removed from your team for the time being, and they both insist on being out of their pokeballs. (When Houndour evolves, you are presented the option of keeping it either in or out of its pokeball.)
With Espeon/Umbreon and Houndour (and any wild pokemon you captured up to this point) you disband Snaggem and learn that there was more to their plot than to kidnap these pokemon. Turns out, they were taking samples of the rare pokemon DNA and sending them off to someone in Kanto. Turns out you're too late, Snaggem has already finished this project, in fact they finished only a little bit after their fortress exploded. Now they're stealing pokemon for their own uses. The culprit now is Team Rocket, who is both using and widely distributing shadow pokemon through Game Corners.
You get a new ticket to Kanto and hop aboard a ship. You stop a Team Rocket plan to raise a signal tower and broadcast their force-evolution radio signal out into the wild, and meet Giovanni along the way. Giovanni, and his Mewtwo, were fighting AGAINST Rocket's plan. Giovanni tells you that Rocket isn't the one behind all this madness and that you should travel to Shinou with him to stop the real mastermind of the plan, Team Galaxy. You tell him about the Game Corner scheme, but Giovanni insists the plan he knows about is a much bigger threat, so you go along with him. Giovanni lets out some massive bird pokemon and flies you to Shinou. There, the Team Galaxy leader has seized control of *another* radio tower and awaits you on the roof of the sky scraper after a long plot. Unfortunately, no matter what you do, Team Galaxy's leader overtakes you AND Giovanni. Easilly. After that, the giant purple Latios/Latias appears and shoves you and Giovanni off the roof of the building you were fighting on. As you fall, a small green pokemon appears to you and asks if you would do ANYTHING to stop Team Galaxy. Angry and without thinking, you say yes. With that, a white light flashes and you find yourself sitting in the grass of Hoenn, safely, and on a beautiful day.
Celebi, the pokemon who appeared to you, has sent you five years into the past. Suddenly, you are unable to access the pokemon you've captured since you don't actually catch them for five more years. The only pokemon you have are the six in your party. (Which include Espeon and Houndoom. After this point, you can remove them from your party.) While you sit in the grass, dazed, a trainer comes across you. His name is Blaize, a breeder and collector (not a very good battler, so don't expect much help in double-battles), who is in the Hoenn region searching for a Latios or a Latias for his ZOO outside the Safari Zone in Kanto. You explain your predicament to him and he miraculously believes you (he has been on Celebi and Mew hunts since he started his zoo and is willing to do anything to meet even one of the two). He sets you up with a new trainer ID so you can capture pokemon again. Then, you set out with him (helping him catch Latios and Latias since you have no idea what you're supposed to do next).
(Blaize captures two Latias and a Latios. Along the way someplace, his wife calls and tells him the pokemon had EGGS even though this is ellegedly impossible.) There is a long plot where you learn some more about Blaize and also learn that Team Magma and Aqua have been particullarly active recently. Turns out, you and Blaize are in Hoenn just in time for Team Aqua and Team Magma's attempts to raise Kyogre and Groudon. Groudon and Kyogre are awoken and start their apocolyptic battle. You are then presented the opportunity to to fight only ONE of these two pokemon (either Kyogre or Groudon). After you CATCH the one you fight, Rayquaza appears and defeats whatever pokemon you did not choose. A new trainer appears out of Team Magma and yells something about how he was "only in it for the Dragon!" and captures Rayquaza. Blaize captures the third legend after Rayquaza knocks it out. The weird Team Magma trainer that captured Rayquaza tears off his uniform and reveals a Galaxy jumpsuit underneath. He lets a Flygon out and flies off.
You and Blaize part ways for a time. Blaize mentions that he wouldn't mind getting his hands on YOUR legend for his zoo. Still, he doesn't ask for it, and leaves. He leaves you alone to sort out where to go next. You still have a ticket for Kanto and Orre (luckilly, they're still both accepted. Handy right?).
Your recent Legend capture airs on the news and shortly after you recieve an invitation from a man in a very nice suit to participate in a rare pokemon "convention." You accept the invitation and go to the Orre region. In Orre, Snaggem appears at the party and steals the party-goers rare pokemon. You go after them and wind up going to the Snaggem base... In doing so, though, you make a mistake. You were trying not to disrupt your own past, but you meet up with your father and he joins your party. YOU blow up the fortress (after kicking Snaggem out, [death toll: 0] and retrieving your Kyogre/Groudon) and make another mistake. Team Snaggem was working on breeding a Latios/Latias hybrid, Latiolas. The explosion sets the giant purple Latiolas free, which again shows the opening sequence. Latiolas wants an explanation for its existance, and is suddenly stricken by a powerful migrane. It flies off (dropping the Snaggem members) after something you can't hear... but your pokemon suddenly can. (Espeon routinely speaks to your mind, and when it starts hearing the signal, all it can say to you is "Johto")
You and your pokemon follow the signal, bringing you to Johto where Team Rocket is force-evolving pokemon (again). You stop them, but learn there are bigger plans afoot. In Kanto, Team Rocket is using the DNA provided by Team Snaggem to clone rare, powerful pokemon, then using the signal to amp up their power even more. (Snaggem then closes their hearts, making the "perfect" pokemon. Follow so far?)
You run back to Kanto where you delibrately avoid the radio tower. You stop in the Safari Zone zoo, looking for Blaize and run into his wife. His wife, a competative trainer (great battler) joins you and brings you to the Celadon Game Corner (the plot Giovanni said wasn't a big enough lead to follow.) You stop them from handing out any more shadow pokemon, procuring a few for yourself (if you want them). (For our purposes, we'll assume Espeon can sense shadow pokemon... so not having Espeon in your party will make it so you can't catch shadow pokemon.) In Celadon, you learn that there all of your leads have one origin: Shinou, just like Giovanni said. Someone in Shinou gave Team Rocket certain crystals they needed to make their force-evolution and force-breeding signals stronger and "untracable." These items were the DIAMOND, PEARL, and OPAL which, despite looking like normal gems, have a consistancy more like glass, and they glow a little bit. Turns out the Shinou leader has a thing for Dragons and used his team to excavate these gems in an attempt to raise Dialga, Palkia, and Giratina. He couldn't figure out what to do, though, but DID find out what these gems could do for Rocket's signals. He sold them to Rocket and continues to make a profit off their operations. Angered, you smash the three gems... which causes an unexpected reaction in Shinou.
With Team Rocket dismissed you, Blaize's wife, and your father move on to the real mastermind in Shinou. Turns out that breaking the gems raised the three dragon pokemon, and they are wreaking HAVOC on Shinou in the wake of their battle. You are again presented the opportunity to fight ONE of these three dragons. You go after one and capture it (or KO it, careful now...), which attracts the attention of the other two. They turn on you, taking you and your pokemon down. Luckilly, two trainers emerge to "save the day." Blaize, and the weird Dragon-Team Magma-guy. The Team Magma/Galaxy trainer and Blaize take down the two pokemon, again each capturing one. The Dragon trainer flees AGAIN without a word.
Blaize arrived because he was drawn to Shinou by the rise of the three legendary dragons. (He wants to capture, or at least see them, for his pokedex/zoo.) Your father is injured in the fight and Blaize offers to take him to a hospital to get patched up. You and Blaize's wife then rush to Shinou's radio tower where you already KNOW Galaxy will be waiting (after all, you've been there before.)
The radio station is already cleared out thanks to Giovanni and your younger self. (Blaize's wife takes one of Blaize's Latios and rides it down to catch Giovanni before he hits the ground. Giovanni is safe.) You make it to the roof just as Latiolas appears and pushes the two trainers off the roof. Latiolas then turns on Galaxy, furious at having been created. (Latiolas is the creation of all this madness: force-bred/evolved, genetically altered, shadow... the "perfect" pokemon.) When Latiolas sees Blaize's wife and Giovanni attempting to circle back, it lifts a shield to keep your helpers from coming back.
Latiolas turns his attention back to the Galaxy leader and tried to kill him. In the interest of protecting a human life, even this scummy human, you attack Latiolas. This battle is different because you can either defeat it, or capture it, but either way its genetics are so unstable it explodes, taking Team Galaxy's radio tower with it. The Galaxy leader is so angry that he forgets all about how relieved he is to be alive. He attacks you with his dragon pokemon (including his Rayquaza), some of which just so happen to be shadow (being Rayquaza and the other legendary dragon). After his defeat, the radio building begins to fall apart. Latiolas' shiled is still just as strong as ever, despite its defeat, which not only keeps other out, but keeps you IN. You and Galaxy's leader make a mad dash down the stairs and try to make it out the door, but the building is falling apart all around you. Suddenly, a beam slices through the building, opening a hole in the wall. You see Celebi again, just outside the new hole. Celebi flies through, gently touches you and Galaxy, and teleports you both to safety.
Giovanni calls Lance of the Elite 4 who, along with your injured father, arrests the Galaxy leader. The world is safe again, thanks to you.
And with all the regions opened, you can go anywhere, catch whatever pokemon they want to make available, and battle every gym leader (and Elite 4, since Lance is in the game, why not?) The End.
Oh, and why not visit Blaize's zoo? After all is said and done I'd have Blaize offer to trade you any of his pokemon for your in-game legends.