The Stratospheric Observatory for Infrared Astronomy (SOFIA) is an airborne astronomical observatory comprised of a 2.5-meter telescope mounted in the aft section of a Boeing 747SP aircraft. During routine operations, several instruments will be available to the astronomical community including cameras and spectrographs in the near- to far-IR. Raw data obtained in-flight require a significant amount of processing to correct for background emission (from both the telescope and atmosphere), remove instrumental artifacts, correct for atmospheric absorption, and apply both wavelength and flux calibration. In general, this processing is highly specific to the instrument and telescope. In order to maximize the scientific output of the observatory, the SOFIA Science Center must provide these post-processed data sets to Guest Investigators in a timely manner. To meet this requirement, we have designed and built the SOFIA Data Processing System (DPS): an in-house set of tools and services that can be used in both automatic ("pipeline") and manual modes to process data from a variety of instruments. Here we present an overview of the DPS concepts and architecture, as well as operational results from the first two SOFIA observing cycles (2013--2014).