The equivalent to Navigation Meshes for 3D spaces is Navigation Volumes.
Havok AI implements both navigation volumes and a volume pathfinder as shown in their GDC 2011 demonstration.
The principle of A* in a volume is the same as A* on a navigation mesh. Since A* will find a path over any graph it doesn't matter if the graph is represented by a point to multiple points, a polygon to multiple polygons, or a volume to multiple volumes. The algorithm will still find a solution if one exists.
Some slight nuances that are different with paths found on navigation meshes is how you determine path points at the edge of line segments, at the ends, or maybe at the middle?
The same can be true of of navigation volumes, to determine the cost to traverse to the next volume you'll typically have to pick a point within the volume, midpoint/edge/etc.
This all essentially boils down to the heuristic part of the A* algorithm you must supply yourself, or use a basic Euclidean distance algorithm.
Path Following is not Pathfinding
How your AI determines to follow this path is something completely different and is referred to as Path Following. The typical strategy for Path Following is to allow your AI to look ahead of where it's traveling to see if it can short cut the path to make more natural curved movements.
Havok AI Demo at GDC 2011
The scene with numerous flying AI's
An inverted view of the navigation volume