My first Pokemon game was Pokemon Mystery Dungeon Blue Rescue Team, so I love all of those games. Their endings have never failed to make me cry when I see them for the first time - and I don't usually cry at stuff. I also loved Pokemon Conquest, and I'd really like to see a sequel.
Out of the main Pokemon games, I think that the Gen 5 games (B2/W2 more than B/W) had a better storyline than most of the other games, but the some of the Pokemon designs were...questionable. *insert Vanilluxe here.*
I liked HG/SS because it allowed you to have your Pokemon walking beside you - I wish they would bring that back sometime!
My favourite main Pokemon game would have to be either Diamond (the first main Pokemon game I beat the Champion with) or Y (even though the characters are just bad, the 3D kinda makes up for that, as do some of the new Pokemon.) I don't have one of the Gen 3 remakes yet as I have to wait for Christmas, but I'll be getting Alpha Sapphire, which may well replace Y as one of my favourite games.