Individual game - Emerald. My first, and Pokémon Ranger did not fill much of the two year gap to Gen IV!
Generation - Gen IV. I own the most games from this generation, and have had many saves on Diamond and HeartGold in particular (I think my highest total hours was on a Platinum save, which is why the plot, gym leader order etc. in my head is that of Diamond). I also owned SoulSilver for about a week before trading it in for HeartGold (can't remember why, may have been to do with version exclusives like Arcane, but Blockbuster did me a straight swap I think which was great). GTS was a game-changer for me, I've never traded a pokémon in-person and until 2011/12 only owned one DS system. The ability to trade all my items, as well as bring resources forward from Gen III, means Gen IV is the one where I EV train (purely to see how good I can get my pokémon, I have nobody to battle except the Frontier Brains), breed for egg moves etc.