Well, shiny Pokemon were not introduced into Pokemon until gen 2 with the red Gyarados, the first shiny poke introduced to Pokemon, and the anime (I think, I COULD be wrong about that) Shiny Pokemon have been in almost every game since then, however some might not be obtainable... For a example, shiny celeb from PMD, she will join your party, but I do not believe she will stay in your teams rooster when you finish the special episode.
It's also like Nobunaga and his shiny Rayquaza from Pokemon conquest (The strategy game introduced some time after Pokemon black and white) His black rayquaza is the only shiny in the entire game, and he is the only one who can get it.
Now, knowing all this, I would say the only games that you can not get a shiny Pokemon is Pokémon Red, Blue, and Yellow (Generation 1), All of the Pokémon Mystery Dungeon games (Except for 2: Pokémon Mystery Dungeons WiiWare, where you can get 36 different shiny pokes, and Pokémon Mystery Dungeons: Gates to infinity, where you can face Pokemon like shiny ho-oh, but can not recruit him) , All of the Pokémon Ranger games, and Pokémon Conquest
I know from playing through these games several times that there is no possible way to get a shiny (Except for the 1 shiny for Nobunaga and I personally haven't played PMD WiiWare but :/ eh~).
However.... Those are some games where shiny Pokemon are unobtainable...
The real Pokemon games where there are NO shinys are: Pokémon Red, Blue, and Yellow, all of the Pokemon ranger games, and PMD Red rescue team, and PMD Blue rescue team
Hope I helped cleared some things up, even though this seems like a big mess~ xD
