What you are really listing are, rather, graph search algorithms, which are a part of Graph Theory. A* happens to be one which is optimized for "pathfinding" applications.
Why bother? Those algorithms are good for much, much more than simple pathfinding. In fact, there is an entire branch of mathematics devoted to studying graph theory and its properties.
BFS and DFS, in particular, are one of the most basic and powerful tools of graph theory application.
EDIT
It is of use to note that A* is rather weak when the shape and nature of the obstacles to be navigated around is dynamic and changing. In this case, it is usually a good bet to look into other pathfinding algorithms.