What is breadth-first search useful for?
Usually when I've had to walk a graph, I've always used depth-first search because of the lower space complexity. I've honestly never seen a situation that calls for a breadth-first search, although my experience is pretty limited.
When does it make sense to use a breadth-first search?
UPDATE: I suppose my answer here shows a situation where I've used a BFS (because I thought was a DFS). I'm still curious to know though, why it was useful in this case.
Answer
When you want to reach a node by traversing as few edges as possible, i.e. when you want to find the shortest path in an unweighted graph.
Also the space complexity of a depth first search can be higher than that of a breadth first search when e.g. each node has only one child node, i.e. when the graph is deep but not very broad.