It's a hard choice. since a a favorite game has to be a game that stands out in all aspects, to me, at least.. Whilst I loved the ever-living hell out of Red when I got it, I have to be honest with myself in that it's graphics are completely out of date, and it was too basic. It was a great game at the time, but the only thing going for it now is the nostalgia. If we're talking about the best game in terms of graphics, no one can deny X/Y, Gen 5 or even Gen 4. In terms of playability, I prefer HG/SS and R/S/E. In terms of story, I really like Diamond. Pearl and Platinum's story, and closely followed by HG/SS.
I think overall, my favorites are HG and SS. They had, and still have nice graphics, it has a huge amount of playability, no one can deny it, it's story is pretty good IMO, and who can deny having a lil' Cyndaquil follow you around?