What sets Halo apart from other FPS series?

Halo Reach has sprinting, as I recall.

But I am surprised that no one has mentioned mix-and-match dual-weilding weapons in the earlier games. Also, sticky grenades. They may seem small, but they put Halo above the competition for it's time. The original Halo also had re-traversing through previous levels that was quite uncommon for FPS games. Instead of simply going from stage to stage, there are points where you have to go back to somewhere that you previously played through to further progress. It also had LARGE, OPEN environments in a time when nearly every FPS was a narrow corridor shooter. Let us not forget all the background chatter of enemies and NPCs in the game. What other FPS did that before Halo? The enemy AI also learned based on your attack. It wasn't just "run into gunfire" or "hide behind a wall" or "suddenly forget they're being shot at." And each time an enemy reacted, it could do something different than it did the last time.

There is a scene in the original Halo where you enter into a large area and on one side is the Covenant and the other side is The Flood. And the characters are going at it while you make your way through them. And what's supposed to happen is that they begin attacking you as you progress. What I did was I simply stayed at the beginning of the stage and literally watched for 10 minutes as the Covenant and the Flood battled each other, listening to the Covenant have random conversations about it... to the point where only a few Flood remained. That's how intelligent the AI in the original game was. The enemy characters killed other enemy characters, but they did it tactically the entire time, and if you wanted to, you could just sit back and watch the whole thing. I doubt the developers intended that to happen that way, but they allowed for it to happen that way.