There is some anecdotal evidence that running barefoot or in minimalist shoes hat some benefits:
Hryvniak, D., Dicharry, J., & Wilder, R. (2014). Barefoot running survey: Evidence from the field. Journal of Sport and Health Science, 3(2), 131 - 136. http://www.sciencedirect.com/science/article/pii/S2095254614000337
It is also a nice training tool for improving your arch stability:
Miller, E. E., Whitcome, K. K., Lieberman, D. E., Norton, H. L., & Dyer, R. E. (2014). The effect of minimal shoes on arch structure and intrinsic foot muscle strength. Journal of Sport and Health Science, 3(2), 74-85. http://www.sciencedirect.com/science/article/pii/S2095254614000374
But of course you must ease into it. A shoe is like a crouch. If you leave them you will limp at first.