(That is to say, Lost stories, not stories which have been lost.)
What is "Mother"'s story? Why did she not want MIB to leave the island?
How did the frozen donkey wheel get completed? Why is it frozen? Why is it claimed (incorrectly, it turns out) that turning the FDW means one cannot return to the island?
What is the story behind the cuneiform script markings on the Source Plug? What's under the Source pool? Where does the water come from? Why does it stop flowing when the Plug is removed? Why does the island start to shake when the Plug is removed? Why does the Man In Black lose his powers when the Plug is removed? What causes the noises that the Source (and the smoke monster) makes?
What happens during Hurley's reign as protector of the island? Why does that reign end? Who takes over from him?
When the characters "move on" from the flash-sideways timeline, where do they go?
Why is the island at the bottom of the ocean in the flash-sideways timeline? At what point in time does it sink (it must be post-Dharma because of the swingset but can't be too far in the future or it wouldn't still be there).
How did Ben's people travel to and from the island?
What was in the box that Ben retrieved from the air vent? Why did he hide it there?
What were the "rules" that Ben and Widmore were following?
What happened at the Swan site between the events of The Incident and Desmond ending up there? What did pushing the button actually do? Who put the hieroglyphics in the countdown timer and why? Why did Radzinsky have the numbers put on the hatch, and why were the Dharma initiative broadcasting them from the radio tower in a loop? Why did Radzinsky commit suicide?
How did the Dharma initiative get formed and find the island?
Who was shooting at the outrigger?
Was Harper alive when she appeared?
Why was Greta and Bonnie's mission kept secret from the other Others?
What were the events leading up to the Purge? How did Ben go from being a member of the Dharma initiative to the leader of the Others?
Who built the Taweret statue and what was their story? Why are there so many hieroglyphic markings on the island?
How did Miles and Walt get their special powers?
What's the story of the Jughead bomb getting onto the island, along with Ellie and Widmore? Were they in the army and did they defect? How were they able to become successful after leaving the island?
What's the story behind the mechanism to summon MIB beneath Ben's house? That's certainly not something Jacob told the Others about.
All the other questions at http://lostpedia.wikia.com/wiki/Unanswered_questions.