2010-2012. Gen 5, the final set of games before Pokemon transitioned to full 3D. Unova was imo one of the most beautiful regions, & BW/BW2 had imo the best storyline of any main series game. DPPt's my favorite still, but I can't deny that the ones that came after blew everything out of the water.
I definitely think the games' story peaked during BW, they were absolutely perfect. <3
For me, things probably peaked around gen III (RSE primarily), I've loved Pokémon since the early gens but my biggest addiction to playing was when RSE were out. I'd have two copies, one as my main and another to replay - every time I beat the league I'd mix records with my and a friend's main game to get the secret base data, then start a new file again. It just never got old.
My second peak was the first half of the BW anime airing. Back then I was addicted to Unova as a whole and just loved Cilan so much lol, I'd have him as a username in some places.