J, H, K, and L photometry for the stars in the central 2' (5 pc) of the Galaxy are presented. Using the observed J-H, H-K, and K-L colors and assumed intrinsic colors, we determine the interstellar extinction at 2.2 mic (A_K) for approximately 1100 individual stars. The mean A_K (= 3.3 mag) is similar to previous results, but we find that the reddening is highly variable and some stars are likely to be seen through A_K > 6 mag. The de-reddened K-band luminosity function points to a significantly brighter component to the stellar population (> 1.5 mag at K) than found in the stellar population in Baade's window, confirming previous work done at lower spatial resolution. The observed flux of all Galactic center stars with estimated Ko (de-reddened magnitude) </= 7.0 mag is approx 25 % of the total in the 2' X 2' field. Our observations confirm the recent finding that several bright M stars in the Galactic center are variable. Our photometry also establishes the near-infrared variability of the M1-2 supergiant, IRS 7.