The framework created by Dungeons & Dragons and its ilk is very versatile, but if you were to base all of your knowledge about RPGs on how they are represented on videogames, no one would blame you if you thought it's just an abstraction for combat. Even in RPGs touted for their story, like Final Fantasy or Mother 3, you spend most of your time fighting things and all your statistics only make you fight things better.

These are the exceptions. They put the role-playing back into RPG, without betraying what a RPG is. You still level up and there are a ton of statistics and equipments, but they aren't used just for bashing things on the head until they stop moving. It does not mean these games are entirely without combat (although some are!), just that it's not the game's focus, and you have other options about how to solve quests and proceed besides fighting.

This list is open to suggestions