We present the results of a search for long-duration gravitational wave transients in two sets of datacollected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9days, respectively. The search targets gravitational wave transients of duration 10–500 s in a frequencyband of 40–1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction,or time of occurrence. All candidate triggers were consistent with the expected background; as a result weset 90% confidence upper limits on the rate of long-duration gravitational wave transients for differenttypes of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upperlimits on the source rate density between 3.4 × 10−5 and 9.4 × 10−4 Mpc−3 yr−1 at 90% confidence. Theseare the first results from an all-sky search for unmodeled long-duration transient gravitational waves.