Lance Runolfsson offers Sci Fi Strat, a set of hex-based science fiction miniatures rules.
Full Command Fantasy Warfare is a set of free wargames rules for hex-based fantasy games.
Hexblitz is a set of free wargames rules for modern-ish wargames on a hex grid.
Anticamente is a set of free hex based rules for ancients offered by TB Line Hobby Wargames. It’s a very nicely presented set. The authors write:
The Rules will let you replay the epic battles that took place from Ancient times right up to the early Renaissance period with an “area-based” approach. The use of hexagons will allow you to use three dimensional scenery in complete synergy with the rules without one aspect penalising the other. Anticamente does not pretend to simulate battles; the unknowns are many and modern deductions are often based on hypotheses which, in turn, derive from a few confused and, at worst, contrasting sources. Instead, after some play tests and objective deductions, Anticamente attempts to suggest the reasons why some situation occurred.
Kampfgrupp OST is a simple Hex based Operational level WWII game circa 1944-1945 East front.