Depends on the system and what you're working on at the time.
If you want to train completely 'realistically', then shoes are a must. However, since I tend to wear steel toe workboots, that could be a wee bit of a problem
The problem is, the potential for accidental injury with shoes on is greater than for the bare foot.
However, it can be difficult to train the correct foot positioning for kicks while wearing shoes. On some surfaces, shoes could either slip or stick to the floor, making footwork difficult.
One in-between solution is tabi boots. They are soft enough so that the ankle and toes have enough movement for correct form with traditional kicks, yet they have some sort of tread and cover the entire foot.
Since I come from a 'traditional' system, I would tend to go bare foot indoors, but occasionally train outdoors with shoes.
Sensible shoes
Cthulhu