There are many Bible stories that can easily be turned into fun lessons for youth groups, such as David and Goliath and the Good Samaritan. The lessons help relate these Bible stories to the challenges of present-day youth, teaching them to use God's strength and be friendly to others.
Any Bible story lesson can be fun with the help of some games that go along with the lesson. Bible trivia, Bible "Pictionary" and many other games can liven up a lesson. There are many online lists of game examples for youth groups, such as ones posted on Pinterest and The Source for Youth Ministry website. There are also plenty of free online resources for Bible lessons at sites such as YouthPastor.com.