In April-May 2003, the blazar 1ES 1959+650 showed an increased level of X-ray activity. This prompted a multiwavelength observation campaign with the Whipple 10 m gamma-ray telescope, the Rossi X-ray Timing Explorer, the Bordeaux Optical Observatory, and the University of Michigan Radio Astrophysical Observatory. We present the multiwavelength data taken from May 2, 2003 to June 7, 2003 and compare the source characteristics with those measured during observations taken during the years 2000 and 2002. The X-ray observations gave a data set with high signal-to-noise light curves and energy spectra; however, the gamma-ray observations did not reveal a major TeV gamma-ray flare. Furthermore, we find that the radio and optical fluxes do not show statistically significant deviations from those measured during the 2002 flaring periods. While the X-ray flux and X-ray photon index appear correlated during subsequent observations, the apparent correlation evolved significantly between the years 2000, 2002, and 2003. We discuss the implications of this finding for the mechanism that causes the flaring activity.