Final Fantasy IX is my second favorite in the whole series. Nearly every aspect of its story and character development are seconded only to VI (in my eyes, VI was a crowning achievement, and laid the ground work for every successful Final Fantasy after it). The characters were deeper and more believable than in other installments; and they ALL experienced genuine growth through the story. The story was epic and lengthy, but did not FEEL long - and aside from the story the mini-games were rich and enjoyable.
But, for me, it still always comes back to the characters -- you felt a commitment to each one, and when any of them had to leave the main party for a while, it was bothersome. When one character effectively became useless because of story events, I know I kept them in party anyway and just slugged my way through it until they were fixed. Each character felt unique in combat as well, and their personality was deeply reflected in their style, abilities and attacks.
Beyond just the characters was a world that was richer than most of the series; with many little details reflected in not only each continent, but the towns between them. The stark differences, yet resounding similarities between the two "tribes" of Burmecia; the odd activities of the Mayor of Dali; the Qu and whatever it is they do...
The closing factor that I always loved was the depth of the themes as well. Kuja, as a villain, was astounding - vilified by factors ultimately beyond his control; and when death looms over him, he experiences such a tremendous existential dilemma.
Over all, the characters, the story, and the flow and interchangeability of each made FFIX a great game, as underrated as it seems to be in the eyes of the world.