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 K_\circ (de--reddened magnitude) \lelt;=q 7.0 mag is ~ 25 % of the total in the 2' * 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.