We present an investigation of the statistical properties of light propagation in a turbulent fluid. Our focus is on the probability density function of the intensity I for different values of I and the beam's path length. The probability density function P(I) exhibits two tails, characterized by stretched exponents, indicating that the likelihood of rare events with intensities much higher than the typical value is significantly higher than naive Gaussian estimates would suggest. We present an analysis of the spatial structure of high-intensity bursts of light.