I've often heard it postulated that the reason adventure paths have become so popular is because many gamers are older and thus lack the time they once had in their younger, more carefree days to allow their campaigns to "grow" a story organically. Thus, adventure paths and similar products give them a "story in a box" that let's them cut through all the "boring bits" they no longer have time for and dive right into what they consider the best part of a campaign: the stories that percolate to the surface through play.
Contrary to conventional wisdom, I'm not opposed to the idea of "story" in a RPG campaign. I happen to believe that the presence of story is where a campaign lives or dies. What I object to -- and what has become the assumption over the last 20+ years -- is that story is something others give you through their products. It's something professionals plot out, write up, and then add pretty pictures to so they can charge you $19.99 for an adventure you can only use once. I see this as the problem nowadays, not "story" as such. At the same time, I recognize that many gamers don't have a lot of time to plan out grand campaign arcs with which their players can interact. That's why I'm offering up the secret of my own success as a referee: make it up as you go along.
Years ago, I ran a campaign that took as its starting point a succession crisis/civil war in a good-aligned country. I decided that, for the civil war to work, I needed to wipe out the entire royal family in one feel swoop, leaving only distant -- and unsuitable -- relations still alive. I did this through the use of a gigantic sphere of annihilation that leveled the palace and effectively decapitated the government of the country, leaving the high nobles, merchant lords, and opportunists scrambling for a way to make the most of the situation. This was the starting point of the campaign, the kick-off that got the ball into play and formed the backdrop for all my subsequent adventures about the players' efforts to restore unity and peace to the kingdom.
Now, that probably sounds like a lot of work to pull off, but, in practice, it wasn't, because I had no idea who assassinated the royal family or why. Neither did I know who would wind up as the new king or queen or how he or she would gain the throne. I left the answers to all these questions up to random chance and the players' actions and, most importantly, inclinations. I knew who the major moves and shakers of the kingdom were and what their personalities were like. That made it easy for me to decide how they'd act during this crisis and they did so. How the players reacted to them and how they interpreted their actions and motives gave me the raw material from which I was able to craft what, in retrospect, looks like a coherent story but what was in fact a spectacular bit of misdirection on my part.
The end result was very satisfying and enjoyable; my players still talk about that campaign till this day, but the simple reality is that I had no idea the whys or wherefores of the assassination or the outcome of the succession crisis -- and that's what made it work. I wasn't imposing anything on the campaign except the initial starting point. The rest all arose through play. And because I had no grand plan, I could freely allow NPCs to die or the players to go off on weird tangents -- like when one kidnapped a nobleman, falsely believing him to have been on the conspiracy to kill the old king -- because, literally, anything was possible until the mass of slowly accumulated details made the identities of the assassins and the best candidate to become the new king clear. This was, if I may say so myself, an awesome campaign and I am very proud of how well it turned out in the end.
The only real drawbacks to this approach are that you must be able to think on your feet and you must know enough about your campaign setting to be able to construct NPCs and "facts" as required. I alleviated some of the latter by having a huge list of prepared names, descriptions, and personalities that I would use at random. That way, when the PCs met someone, he wasn't obviously generic-merchant-lord-who's-unimportant-to-the-plot but instead Maynoor Misrim, a tall distinguished gentleman who speaks with an imperious manner and walks with a slight limp. In short order, I had a huge cast of NPCs, any one of whom might be important, depending on how the PCs acted and how the dice would go.
In play, this approach took very little planning and I kept it going for months without much effort. I realize it's not for everyone, but I heartily recommend it nonetheless. Most of my best and most memorable campaigns ove the years have used this approach and I fully intend to use it again in my future ones as well.