The assumption that multivariate data are (multivariate) normally distributed is central to many statistical techniques. The need to test the validity of this assumption is of paramount importance, and a number of tests are available.
A recently released R package, MVN, by Korkmaz et al. (2014) brings together several of these procedures in a friendly and accessible way. Included are the tests proposed by Mardia, Henze-Zirkler, and Royston, as well as a number of useful graphical procedures.
If for some inexplicable reason you're not a user of R, the authors have thoughtfully created a web-based application just for you!
Korkmaz, S., D. Goksuluk, and G. Zarasiz, 2014. An R package for assessing multivariate normality. The R Journal, 6/2, 151-162.