After some friends introduced me to 13th Age I discovered I like it. There's not as much detail as in D&D (3-4), its rules are more streamlined (without being the IMO oversimplistic system in D&D 5/Next), but, above all, the system forces you to think about the character.
I have read and heard a lot of complaints about D&D 4, how it "prevented" the players from getting into character with all the skill challenges and the encounter-block-kind-of-adventures, and I have long pointed that the system actually doesn't prevent from acting, just starts rewarding as heavily the roleplaying as it did the combat. That it's material for another post, but what I want to emphasize here is that 13th age's system you are kind of forced to think about your character by two core things:
1. The Unique Thing: every player character has something that marks him apart from every other member of its race and class beyond game traits, feats and other customization. What's more, being a unique thing it means it allows the player to intervene in how the campaign world is. A few examples of how to do that are given in the core book. If your character is the only halfling in the Emperor's legions, then there's no one more. In other worlds, in other campaigns, in other teams there could be, I don't know, a imperial halfling scout platoon, but not in yours. See what just happened? Now there's another world in which there exists the Imperial Flying Stones, a halfling scout platoon.
What's more interesting of the Unique Thing is that it can't have mechanical effects. Story effects? Sure, of course; just not mechanical.
2. The Backgrounds: instead of a skill system 13th age tries to make you think how, where and/or why your character knows what it knows. For every character class they suggest a few cool inspiring background examples, like barbarian's Wolf Tribe Member but above all encourages the player to invent the ones for the character. My first character was a fighter from the Gray Imperial Legion who had participated in a joint forces thing with a Dwarf King's army's platoon.
The backgrounds are as open as the players and the GM (gamemaster, just in case) accept them. I could have used my background with the dwarven army to understand a few dwarven words or to improve how well I can find my way in a dwarven city or the big cavern networks so frequent in these kind of games.
So, yeah, no game system prevents you from roleplaying, but there's at least one that forces you to.