A commonly known thing that you didn't know.
A time you got in trouble.
Childhood dreams (e.g. what you wanted to be when you grew up).
Compelling / dramatic stories about your life.
Creative works (e.g. published a book)
Cultural experiences (e.g. organizing a dance festival)
Disadvantages / Adversity
Disappointments / Things you learned
Dreams / Goals / Vision for your life
Experiences living abroad
Failures / How you recovered
Favorite animals / Pet related stories
Favorite art + why
Favorite color + interesting story
Favorite film / series / director / actor
Favorite season + why
Fears / Fears you've overcome
Funny stories about your life
Inspirational moments / Sudden realizations
Languages you speak
Likes + interesting story
Passions / Obsessions
People you know
People you've helped
People you've met (i.e. interesting story -- avoid name dropping)
Problem's you've solved
Sense of humor
Sense of imagination
Skills you've mastered
Sports you play
Sports you watch / Teams you support
Style / Fashion sense
Subculture pursuits (e.g. cosplay)
The people who helped you / Stories of gratitude
Things you'd do differently
Things you've lost
Times you surprised yourself / the people who know you
Times you were brave
Traditions you follow
Values (e.g. a story about how much you value your independence)
Ways you've changed
Specific ExampleA good answer to the question of "what is interesting about you?" could be humble and mildly humorous but also communicate something noble about you.
In high school I tried to make the cross country team three times and three times I failed. They must have liked my persistence though, because when the star runner broke their ankle at the start of a season, the coach invited me to join. I'd like to say that I went on to win championships for the school but that wasn't the case. However, it became a great experience for me as I enjoyed being part of the team and eventually improved from placing around 30th to placing in the top 10 in several races.