Look at the characters you have, and make stories based on their history and goals?
I had fun starting a campaign with a competetive dungeon crawl event, hosted by jaded upper class mage's society, a maze with several entrances for various parties, that narrows out, forcing the parties to interact, ally or assassinate each other. The final challenge was a sphynx construct, had to place one hand in its mouth to give your final answer to its riddles, it removes the hand if answered wrong, 3 right answers for a party to win. Or best it in combat instead. The game started on the road to it, some random adventures as they came together in ones and twos, met by chance and bonded by lust for gold and glory.
Also, escaping from a slave caravan or ship or a prison cell is always fun, leading to a campaign of escaping or destroying your ex-captors.
This won't work until characters have magic items, but I've been having a lot of luck generating stories lately by making every magic item unique and having one flaw/drawback for each. Brainstorming about why this weapon was made and why it has a specific drawback leads me to asking all kinds of questions with many interesting results.
A few examples:
2. A new player joined the group at level 6. I told him to give himself two minor magic items, but each must have a drawback. He said he had an invisible tent, but that every time a group used it, some random item went missing for 6 days. I dialed that back a bit and made it 1d6 days. Their first usage saw the disappearance of a druid's scimitar. I started asking myself, where did it really go? What if it comes back bloody? Now I have some mastermind assassin's guild crime boss out there whose magic tent, in the hands of an unwitting PC, is delivering weapons and/or whatever else his loyal followers may need to carry out their nefarious deeds. It's only a matter of time before a witness to the king's murder recognizes the murder weapon in the hands of the hapless party. That is, if I run out of story lines to pursue. Always in my back pocket, that one.
3. A bag of holding. Read the item description: it opens to a "non-dimensional space," whatever that means. I don't see why another bag of holding can't open to the same "space" (saw this idea develop on another thread). Maybe it's a matching set of three bags? And what happens when one of the other bag holders takes something out that you put in, or vice versa? Or you reach in and there's a hand groping around? Or a claw? All you have to do is think about the other two peeps who have the bags, create a percentage chance for these kinds of events, and watch the adventure take care of itself.
4. Do something non-sensical and let the players figure out what's next. I put a giant lemur's paw in the bag of holding. It radiates a faint aura of magic. All their spellcraft and knowledge arcana rolls are for naught, and they don't have Identify. It's driving them nuts. They're going to try to figure this out when they get to town, which won't be for a while. All it is is a paw with an extremely valuable emerald sewn up inside, and Magic Aura cast on it to throw people off. Whoever they pay to Identify it will say it is worthless, or valuable only to alchemists, or some such nonsense, and try to separate them from it. If he succeeds and goes on a spending spree, what will the characters do?
I start with random treasure generation tables, then ask myself the questions later. I also let the players' questions guide me. You can take this technique and use it on things other than magic items, with a little imagination.
TL;DR Don't write stories. Write questions, and let them lead you where they may.
Good luck :)
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1. Starting with some setting specifics helps. Every city needs warring families. Every outpost needs mystical wilderness…
2. Add a theme. Espionage. Hack and slash. Survival. Camp…
3. Add characters. NPCs that make sense in the setting and theme…
4. Give these NPCs reason to interact with the PCs or vice versa…
All along the way plagiarize heavily, tailor the story to the PCs, and let them make story for you.