Hex is likely the most famous early application, circa 1942.
This article Games for Three lists Three-Handed Hexagonal Chess as first developed in 1912 by by Sigmund Wellisch.
- Are there earlier applications of hexagonal gameboards?
Stern-Halma (aka "Chinese Checkers") is the earliest application I've found so far. Although the board is not formally divided into hexagons, the center region allows 6 directions for movement from a single cell. (This is allowed because the tokens are place in the intersections of triangles--triangles seem to have preceded hexagons for three-player variants of popular combinatorial games.)