Following the detection of strong TeV gamma-ray flares from the BL Lac object 1ES 1959+650 with the Whipple 10 m Cherenkov telescope on May 16 and 17, 2002, we performed intensive Target of Opportunity (ToO) radio, optical, X-ray and TeV gamma-ray observations from May 18, 2002 to August 14, 2002. Observations with the X-ray telescope RXTE and the Whipple and HEGRA gamma-ray telescopes revealed several strong flares, enabling us to sensitively test the X-ray/gamma-ray flux correlation properties. Although the X-ray and gamma-ray fluxes seemed to be correlated in general, we found an ``orphan'' gamma-ray flare that was not accompanied by an X-ray flare. After describing in detail the radio (UMRAO, VLA), optical (Boltwood, Abastumani), X-ray (RXTE) and gamma-ray (Whipple, HEGRA) light curves and Spectral Energy Distributions (SEDs) we present initial modeling of the SED with a simple Synchrotron Self-Compton (SSC) model. With the addition of another TeV blazar with good broadband data, we consider the set of all TeV blazars to begin to look for a connection of the jet properties to the properties of the central accreting black hole thought to drive the jet. Remarkably, the temporal and spectral X-ray and gamma-ray emission characteristics of TeV blazars are very similar, even though the masses estimates of their central black holes differ by up to one order of magnitude.Comment: Accepted for Publication in the ApJ on October 2nd, 200