Dating sims, raising sims, and other "social simulation" games. Common elements include stat management for the protagonist and turn-based schedule management. The stat systems can resemble other RPGs, but govern interactions beyond combat (or exclude distinct combat phases completely).
If there's titles I've missed, you can reach me at stepnix401(at)gmail(dot)com
This might be too much of a management sim to count but i'm playing it safe
This might be too much of a business sim to count but i'm playing it safe
Demo for a full game purchasable elsewhere