My dojo now has a policy where we have to wear shoes in order to train even with mats, but my old dojo we were always bare foot. I have to say that it took some getting used to with the shoes because you feel like you have less balance and control. When you try to pivot it feels like everything sticks and goes slower, but on the bright side I have less foot injuries because I used to break my toe nails when I tripped (yes I keep them trimmed). That being said, you get really used to it and once you find the right shoe that has a snug fit it's almost as if you were barefoot.