I just thought of this when I paid yet another visit to TV Tropes. Someone there mentioned that Demyx was basically treated as a one note character in 358/2, and because of that, couldn't understand why he is so popular(Demyx has always rivaled Axel and Roxas in terms of popularity). I can tell you why. I can give you five reasons why. Easily, in fact.
Top Five Reasons why Demyx is SOOO popular.
1. He's cute. Yes, he is very cute. Fandom can be pretty shallow, and nine times out of ten, an underdeveloped good-looking character trumps a developed not so good looking one. The mullet helps a lot too.
2. Plays the sitar/stringed instruments and has a rock star image about him. Fandom loves this.
3. He is expressive. This is one of the reasons why he stands out in Organization 13. He and Axel are considered the most emotional of Org 13. Not bad for those who "lack hearts"(that depends on what you mean by "heart" though). He's either a damned good actor or he really does have a greater range of emotions that most of Org 13. Fandom eats this for breakfast.
4. He is far less evil that other Organization members. The way he "fades" hints this because he fades into light. No one else in Org 13 does. At least not that I recall. Whatever the case, he's different. Fandom likes different.
5. Those who provide comic relief are often very popular, especially IF THEY'RE CUTE. It helps that it's widely believed that there's more to him than you think. More fan fodder.