The WMAP satellite has completed 3 years of observations of the cosmic microwave background radiation. The 3 year data products include several sets of full sky maps of the Stokes I, Q, and U parameters in five frequency bands, spanning 23-94 GHz, and supporting items such as beam window functions and noise covariance matrices. The processing used to produce the current sky maps and supporting products represents a significant advancement over the first-year analysis and is described herein. Improvements to the pointing reconstruction, radiometer gain modeling, window function determination, and radiometer spectral noise parameterization are presented. A detailed description of the updated data processing that produces maximum likelihood sky map estimates is presented, along with the methods used to produce reduced resolution maps and corresponding noise covariance matrices. Finally, two methods used to evaluate the noise of the full resolution sky maps are presented along with several representative year-to-year null tests, demonstrating that sky maps produced from data from different observational epochs are consistent.