I got this from Sagie Davidovich a link to Kaggle's Titanic Contest. The task is to predict who survived the Titanic based on some features like age, cabin class, name, and presence of relatives on the Ship.
What I like about this task, is that you can actually explain to your gradma what you are predicting (unlike many other ML tasks which are hard to explain for the non expert..). The dataset is quite tiny in our standards. But still enables the usage of different ML methods. The best prediction on the leader-board has about 99% accuracy.