I really enjoy Firered/Leafgreen the most. Gold/Silver is close, but I can keep replaying through Kanto without getting bored unlike anything after gen 2.
Sapphire and White are tied as my favourite. I love Sapphire because it was my first Pokémon game and will always have a place in my heart, and White because it was the game that got me back into Pokémon after I lost interest in it for a while. I also enjoyed the story, and the Unova region as a whole.
Gen 2 is my favorite, but I also like the Mystery Dungeon series, with Explorers of Sky being my favorite of those.
As far as main series games go, it's a tie between Emerald and Platinum. Although if this is asking my favourite Pokémon game of all time, that would have to go to PM Explorers of Sky, with Pokémon Colosseum being a very close second. So many memories with both games. @_@
Pokémon Gold. I think it was the first game I played, and I feel like it just has the most to do of the games that I have available to me, though considering that's just Gold, Ruby, and Red, that's not really saying much. Someday I'll play past gen 3, but until then I'm kinda content with Gold.
The Pokémon Mystery Dungeon games are the best, especially the Explorers games. Quickly following is Pokémon Conquest.
I'd say my favorite is my first main series game, Pokémon Black. Followed closely by Ultra Moon, followed by Moon, followed by my first Pokémon game ever, Pokémon Rangers: Guardian Signs.