Damage [Elemental & Weapon] Type Systems

I'm getting into Octopath Traveler these days [I know, I know: I'm behind the times], and I'm simultaneously enjoying the variety of physical damage options from the various weapon types and disliking the fact that weapon types that Dungeons & Dragons simplifies into Bludgeoning, Piercing, & Slashing get separated into many more types.

Anyway, with that preamble out the way, I'm curious what damage type systems are out there, as well as which ones you all like and dislike--and why?