Uzirath great post and approach to introducing young students to RPGs. I'm also excited about @Grendel_Khan suggestion of Scum and Villainy. I went ahead and ordered that to read and play as well.This rings true for me, too. As a middle-school teacher who sponsors the school RPG club and runs an RPG summer camp, I introduce a lot of young people to the joys of this hobby. But, I was weaned on D&D and have absorbed many of its tropes, so my default style of play includes a fair amount of combat. I've often been surprised by the young folks who start playing for the first time. Some of them, having played tons of CRPGs, enter the game world expecting to battle their way to glory. Others are bemused or even put off by this approach. They're much more interested in finding clever solutions, creative compromises, and non-violent options. They often want to learn about the monsters' cultures and find out what they want out of the world. They expect the game to support and encourage that sort of fiction.
As I've evolved with running the club and summer camp, I've de-centered violence as much as possible. It's there for those who want it, but we don't present it as a necessary component of an RPG. This has gone over pretty well, though plenty of groups retain a murder-hobo aesthetic.
The game I am most familiar with these days is GURPS. Although it includes a potentially intricate combat system, the default system is deadly, so there is a disincentive to be casual about it. It is also a skill-based system that covers a wide array of genres, so it's easy to focus on social conflict and other subsystems. I've played in games with little or no violence. I, myself, have been most comfortable running the dungeon fantasy flavor of GURPS, which tunes things to encourage more battle (and makes it relatively difficult for PCs to die). I'd like to move my own campaigns away from this, but I often fall back on familiar tropes.
Based on @Grendel_Khan's suggestion above, I picked up a copy of Scum and Villainy and started reading it last night. It reads well and I look forward to trying it out for a change of pace.