I very much enjoyed the cut scene in Emerald with the three mascot legendaries. I think that was the first cut scene in any mainstream Pokemon game.
But I actually really enjoy traveling around the area of Hoenn where the rain/drought is happening before I go to Sootopolis City to resolve the problem. I always thought that was neat. I remember being blown away by overworld weather effects anyway, as well as being able to see my reflection and the sky in the water and stuff.