Abstract : In this paper, we examine properties of the variable source Sgr A* in the near-infrared (NIR) using a very extensive Ks-band data set from NACO/VLT observations taken in 2004-2009. We investigate the variability of Sgr A* with two different photometric methods and analyze its flux distribution. We find that Sgr A* is continuously emitting and continuously variable in the near-infrared, with some variability occurring on timescales as long as weeks. The flux distribution can be described by a lognormal distribution at low intrinsic fluxes (lsim5 mJy, dereddened with AKs = 2.5). The lognormal distribution has a median flux of ≈1.1 mJy, but above 5 mJy the flux distribution is significantly flatter (high flux events are more common) than expected for the extrapolation of the lognormal distribution to high fluxes. We make a general identification of the low-level emission above 5 mJy as flaring emission and of the low-level emission as the quiescent state. We also report here the brightest Ks-band flare ever observed (from 2008 August 5) which reached an intrinsic Ks-band flux of 27.5 mJy (mKs = 13.5). This flare was a factor 27 increase over the median flux of Sgr A*, close to double the brightness of the star S2, and 40% brighter than the next brightest flare ever observed from Sgr A*.