This thread really should be updated to include Black/White 2 and now X and Y to remain up-to-date.
Also, I'm gonna update my answer from over a year ago. I don't really enjoy SoulSilver all that much anymore, as I've become accustomed to the more dynamic in-battle movements of the 'mons and of the much higher levels found within the newer games. Also, aside from Voltorb Flip (still one of my favorite sidegames btw!) there just really isn't anything to do after you beat Red.
So yeah, I'm updating my answer to a tie between Emerald, Black 1, Black 2, and Y.
Emerald, still same answer as before. Same as Black 2.
As for Black 1, while it also suffers the same fate as SS in that there really isn't much to do at a certain point after beating the League (for real), and while I still don' really care that much for a great deal of the Gen 5 designs, and while there really isn't much sidetracking from the main story of the game, I can quite easily forgive Black 1 of these transgressions because the main story's just that darn good. Seriously, it's the only Pokemon game I picked up to play through for story reasons rather than gameplay as is default for me. I honestly think GameFreak outdid themselves with it, because I'm having a hard time thinking of how they can outperform it.
[For this next bit, SPOILERS AHOY! Ye be warned!
And as for Y, I only really need to say this: POKEMON BATTLES IN 3-D!!! The visual design of Pokemon games has never looked as good as this, and it's just a blast to watch them duke it out in fully-rendered 3D combat. On top of that, the much-improved online capabilities have been a godsend for me in improving my own competitive strategies. But battling isn't the only thing X/Y have going for it either! I quite enjoyed the story of Y as well, and while the villainous team didn't reach for quite the same levels as Plasma did, they still had their own sense of style that I found captivating, as well as a central motive that turned out to be far more disturbing than I originally gave them credit for (if my avatar is anything to go by, I'm quite smitten by the blokes). As well, I was also enthralled by your friends/rivals that traveled alongside you and each had their own motives for doing what they did (my favorite among them being Shauna, since she had the most personality of the bunch and also seemed to have a thing for the main character which I found just adorable
) Not to mention AZ and the backstory of the Great War (I'm glad they managed to work a global war into the Pokemon games, though I still maintain that it'll be freakin' sweet if we as players get to take part in that war).
And, as a blanket statement for all 4 of the games, the music for each is superb, each of them in their own ways.