Simple
I actually think if you're looking for a little more bite in your "simple" game, 5th edition D&D is a very clean system, especially at early levels.
If you're looking for a simple system, a lot of the Greatest Hits of minimalist games have been named.
Once you roam past minimalist games, you start getting into Narrative games. A lot of narrative games, despite having simple mechanics, are tricky to play, since they rely on a good understanding of narrative roles, and storytelling and roleplaying techniques. FATE is probably the most popular narrative game, but a lot of the indie darlings (that aren't minimalist) fall into this category.
If you want a game with some bite but not as dense or complex as, say, D&D, you can lighten up on the rules with games like WoD, Savage Worlds, and Dungeon World.