Its very rare for a quest to be failable and for you to still continue playing. Most quest failures end a bad ends. That being said, there are a few cases where you can fail a quest and continue.
Ugly Duckling: Lose to the golem. This is actually hard to do because the golem fight is trivial even at level 3.
Shades of the Past: Decline the quest or Lose a fight. Bring/Be a healer, eat a trail ration, and be at least level 4 and you'll be fine.
There are a few instances where you can be a dick and get a less optimal result, but the quest will still be considered completed. Such as right of conquest where you can ambush Argoth or leave instead of hiding a watching.