We present the results of a 3.3-year project to monitor the flux density of Sagittarius A* at 2.0, 1.3, and 0.7 cm with the Very Large Array. Between 2000.5 and 2003.0, 119 epochs of data were taken with a mean separation between epochs of eight days. After 2003.0, observations were made roughly once per month for a total of nine additional epochs. Details of the data calibration process are discussed, including corrections for opacity and elevation effects as well as changes in the flux density scales between epochs. The fully calibrated light curves for Sgr A* at all three wavelengths are presented. Typical errors in the flux density are 6.1%, 6.2%, and 9.2% at 2.0, 1.3, and 0.7 cm, respectively. There is preliminary evidence for a bimodal distribution of flux densities, which may indicate the existence of two distinct states of accretion onto the supermassive black hole. At 1.3 and 0.7 cm, there is a tail in the distribution towards high flux densities. Significant variability is detected at all three wavelengths, with the largest amplitude variations occurring at 0.7 cm. The rms deviation of the flux density of Sgr A* is 0.13, 0.16, and 0.21 Jy at 2.0, 1.3, and 0.7 cm, respectively. During much of this monitoring campaign, Sgr A* appeared to be relatively quiescent compared to results from previous campaigns. At no point during the monitoring campaign did the flux density of Sgr A* more than double its mean value. The mean spectral index of Sgr A* is alpha =0.20+/-0.01 (where S nu \propto nu ^ alpha ), with a standard deviation of 0.14. The spectral index appears to depend linearly on the observed flux density at 0.7 cm with a steeper index observed during outbursts. This correlation is consistent with the expectation for outbursts that are self-absorbed at wavelengths of 0.7 cm or longer and inconsistent with the effects of simple models for interstellar scintillation. Much of the variability of Sgr A*, including possible time lags between flux density changes at the different wavelengths, appears to occur on time scales less than the time resolution of our observations (8 days). Future observations should focus on the evolution of the flux density on these time scales.
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