We report the first results of a study of variable point sources identified using multi-color time-series photometry from Sloan Digital Sky Survey (SDSS) Stripe 82 over a span of nearly 10 years (1998-2007). We construct a light-curve catalog of 221,842 point sources in the R.A. 0-4 h half of Stripe 82, limited to r = 22.0, that have at least 10 detections in the ugriz bands and color errors of < 0.2 mag. These objects are then classified by color and by cross-matching them to existing SDSS catalogs of interesting objects. We use inhomogeneous ensemble differential photometry techniques to greatly improve our sensitivity to variability. Robust variable identification methods are used to extract 6520 variable candidates in this dataset, resulting in an overall variable fraction of ~2.9% at the level of 0.05 mag variability. A search for periodic variables results in the identification of 30 eclipsing/ellipsoidal binary candidates, 55 RR Lyrae, and 16 Delta Scuti variables. We also identify 2704 variable quasars matched to the SDSS Quasar catalog (Schneider et al. 2007), as well as an additional 2403 quasar candidates identified by their non-stellar colors and variability properties. Finally, a sample of 11,328 point sources that appear to be nonvariable at the limits of our sensitivity is also discussed. (Abridged.)