Most of the people don't know how the intial success of World of Warcraft did happen. I would like to mention some points why the game did become so popular. Feel free to add more or discuss.
1) Warcraft 3 - most of the new players don't know what Warcraft 3 was or they knew, but they have never played it. Warcraft 3 was one of the greatest strategy games of all times and without doubt it was the best strategy game of its era. This game was revolutionary in every aspect, it had great graphics, gameplay, amazing music and sounds, great map editor and let's not forget the great story it had. I can say that the majority of vanilla WoW players(me included) played a lot of Warcraft 3. We all wanted to visit great places from game, explore them, do the quests and do it with your friends or even other random people. I can't even describe how if felt when I visited Ashenvale or Barrens - it was beyond amazing.
btw there was bonus campaing in Warcraft 3, where you played as Rexxar and did quests given to you by NPCs, while you were gaining levels and items. Does it sound familiar?
2) Leveling - people tend to hate on vanilla WoW leveling, but I have to disagree with them. Yes, leveling was tought, but we loved it. Mobs had high hp pools and were hiting for a lot, pulling more than two will most likely result into corpse run. You had to actually use your brain, develop a strategy and use all your class abilities effectivelly to level up quickly. Even AH was very important for quick leveling. Quests were very simple, but most of the time you felt like part of the world and you even felt like you are helping npcs - like in real RPG
3) Social aspect - As I mentioned, leveling was pretty hard and the best way to make it easier was to group up with other players. I like how friendly people during vanilla WoW were. You could just talk to random person and 95% of time he would respond in friendly way. I've mad countless friends in vanilla.
4) No addons - yep, there were almost no addons and it was great. You don't know where the quest mobs are? Ask friends, guild or even general chat. Try to do this in WotLK or Cata, you would get typical "google it, use wowhead" answer. Addons are taking the fun factor out of the game. Why are people using addon to help them with rotation or addons like DBM? That's just silly.
5) RPG aspect - Why am I mentioning this? Back in a day... No, seriously. Back in a day you had to carefully choose your class and stick with it. There were no alts, only some people who played a lot could afford this luxury. Your character was part of you, you were part of your character. It was great, because this game is RPG after all and not just some Dota or LoL game.
Why am I writing this? I just want to tell people that WoW wasn't always only about raiding, arena and daily quests. It was far more. Game had soul, it felts like RPG and leveling was important and possibly the best part of the game. The true mmorpg.