They make changing behavior dynamically extremely simple. Instead of needing to hardcode classes for each different type of thing players may want to create in your world, you just assign and unassign components. Give a rock the Moveable component and now it moves. Remove the PlayerControl component from the player and put it on, I don't know, an orc -- now you've implemented body swapping. They're even more useful in a game like traditional roguelikes, where you don't have to worry about animating all these dynamic states.
I've actually never thought about how a component system might fit into a more traditional business application; it's an interesting thought experiment but I'm not quite sure it would be a strong benefit.