A breadth-first search may outperform A* when the heuristic is inconsistent. (An inconsistent heuristic doesn't obey the triangle inequality. A consistent heuristic never changes more than the edge cost from one state to the next.)
With an inconsistent heuristic A* may expand N states up to 2^N times. The example of where this occurs can be found online. Step through the example if you want to understand what happens. BFS will only expand each state at most once. Note that this can be partially fixed by algorithm B (N states expanded at most N^2 times), but this is still a large overhead. The recent IBEX algorithm has much better worst-case guarantees - N log C*, where C* is the optimal solution cost.
A depth-first search may outperform A* and BFS if the goal is on the first branch. In this demo you can place the goal at different states in the tree to see what happens.
There are other constant factors to consider. DFS only needs a single copy of a state, while A* keeps many states on the OPEN/CLOSED lists. But, in these cases IDA* should be used instead.
Note that theoretically speaking, in unidirectional search with a consistent heuristic, A* does the fewest number of necessary expansions required to prove that the solution is optimal.