The ALICE experiment at the LHC requires a data acquisition system capable of handling both frequent small events from proton-proton collisions and rare but large events from heavy ion collisions. The ALICE DAQ system uses over 300 front-end processors to collect data from detectors at up to 2.5 GB/s and store over 1 PB of data per year using a multi-tiered storage architecture. Regular data challenges since 1998 have tested the DAQ system and achieved event building rates over 1 GB/s.