GenIII... Where should I start...
Personally, out of all the Pokemon games I've played, none can compare to the playtime on my Emerald.
Emerald's also the only one with the most complete PokeDex, plus all extra features such as Master Level at all contests, thus pictures in the Museum, as well as all the Frontier badges.
Also, Gardevoir.
TRAP GARDEVOIR EVER
Ok, but seriously, story-wise, as some as mentioned, had the villian team finally succeeding in what they set out to do (more so in Emerald), as well as the introduction of legendaries that had a direct impact in shaping the Pokemon world.
Personally, I'm biased to the 3rd Gen, due to the most number of favourite Pokemon in there.