Vanilla WoW may not have seemed full of story to most, but it was jam-packed with plot elements, although they were hidden from all but those who paid the closest attention to what was going on around them. Most lore in the game was simply introduced with quest text -- there were no cut scenes, there was no phasing, there were none of the innovations we currently have today in regards to the implementation of lore in gameplay.
If you missed them, I recommend going back and reading through the summaries of early days of vanilla lore. There are two versions of Act I, one for Alliance and one for Horde. Act II applies to both sides of the faction fence as the story began to merge for both sides. Please note that these are summaries of the lore that existed in game -- later novels, comics, and other material adjusted what actually happened in the scope of the game universe, and some of those novels and comics are now the official canon version of these events. I've pointed out where these changes occurred.
The end of vanilla was marked with the return of foes long thought dead and gone, and the ominous stirrings of a portal to another world.