It's a waypoint/checkpoint system, but I have code that gives it all the functionality of A*.
It can manage active objects (ie. lockable doors, blockable passages). It can work in full 3d (eg. flight games) and also in games where you walk around a 3D world (eg. FPS, RTS, RPG, etc.). It isn't a rigid system (ie. if a character is forced off course, he won't waste time trying to get to where he was going if there's a shorter/safer route). It handles tactical positioning (so you can find tactical positions when attacking/hiding from enemies). It doesn't let you walk off of cliffs (unless you want to, as there's an override).
That's basicly all you need from a routing system, and it's an easy to use interface for setting up the checkpoints and for using it while programming means that a total novice to AI can get to grips with it within minutes; although it is also powerful enough for the more seasoned programmers.
Are there any other features that A* has that I haven't listed? If so, I'd like to add them to my program.