KDD Cup is the annual Data Mining and Knowledge Discovery competition organized by ACM Special Interest Group on Knowledge Discovery and Data Mining, the leading professional organization of data miners.
Below are links to the descriptions of all past tasks.

KDD Cup 2010: Student performance evaluation
KDD Cup 2009: Customer relationship prediction
KDD Cup 2008: Breast cancer
KDD Cup 2007: Consumer recommendations
KDD Cup 2006: Pulmonary embolisms detection from image data
KDD Cup 2005: Internet user search query categorization
KDD Cup 2004: Particle physics; plus protein homology prediction
KDD Cup 2003: Network mining and usage log analysis
KDD Cup 2002: BioMed document; plus gene role classification
KDD Cup 2001: Molecular bioactivity; plus protein locale prediction
KDD Cup 2000: Online retailer website clickstream analysis
KDD Cup 1999: Computer network intrusion detection
KDD Cup 1998: Direct marketing for profit optimization
KDD Cup 1997: Direct marketing for lift curve optimization