List of quests for F2P players:
Black Knight's Fortress
The Blood Pact
Ernest the Chicken
The Knight's Sword
Myths of the White Lands
Prince Ali Rescue
The Restless Ghost
Shield of Arrav
Please note that tasks are not the same thing as quests. A quest is somthing given out by a person (not a player) in runescape. A task is like a quest except for 3 things.
1. For most city/areas in runescape there will be a set of tasks to complete, And once each set is complete you can pick up some reward.
2. Tasks are not given out by the computer generated people. Tasks are listed and you may complete some of them without speaking to anyone.
3. ONLY quests give out quest points. Tasks do NOT give out quest points. After each task you may be elegible for some reward:gold, some item, etc. But you will only get quest points from doing quests.