Well, I can't choose from all the Pokemon games there are, but my favorites would be LeafGreen and HeartGold. LeafGreen, because I just can't get enough of text box that was used in the game (I'm a complete nerd for text bars in Pokemon games T_T), I love how before you start playing the game, a little preview of what you've done last in the game is shown, and (this is a pretty stupid one) how whenever a NPC says something important, the text shows up in red instead of blue. I found that useful. :B
I like HeartGold because of the follow me feature with your Pokemon, the addition of the red text for a lowered stat, and blue text for a heightened stat due to the nature of your Pokemon, being able to travel between Kanto and Johto, the music, the storyline, and the comeback of Team Rocket.
I never got to play Emerald (only got Sapphire), and I heard that the storyline in Emerald is much better than R/S. Wish I could've played that game. =/ (Hopefully there will be remakes...)
Oh, and if spin-offs count, then MD: EoT is also a favorite. I loved the storyline and music, and it was just overall fun to play. :3