My favorite is Pokemon Emerald. When choosing a favorite Pokemon game, a lot of what I take into consideration is post-game content. I don't want to just beat the Elite four and be done with the game, yknow? I want to have fun with whatever happens after the game, I want to see more of what the game has to offer. Truth be told, I want the experience of going on another adventure post-game. This meaning that I only want the main storyline to kind of be a small part of what the game is really about.
Of course, Emerald isn't a shining example, since the Team Magma/Aqua conflict was pretty big (and the inclusion of Rayquaza made this even more so, which I have no problem with because it was executed quite well), but what I'm speaking of is the Battle Frontier. To me, Emerald has, hands down, the best Battle Frontier in any main series Pokemon game, where one could continuously challenge the Battle Pike, or the Battle Pyramid, and hardly get tired of it because of the challenges that they pose. Sure, HG/SS has a decent frontier, but I feel it pales to the real challenges and conditions that Emerald offered. I mean, for goodness sakes, I'm pretty sure there's a battle facility where your pokemon battle completely on their own. I really miss that, and I hope that it makes a return someday.
But yeah, Emerald will forever be a part of my memories because of how much fun not just the storyline was, but post-game as well!