The island-themed, first-person shooter Far Cry Instincts for the Xbox isn't currently playable on the 360. This is relevant because, although this 360 game gets its own name, it's really an upgraded and bundled version of Instincts and its expansion pack, Far Cry Instincts Evolution. It's actually a great value for the money, just as long as you don't already own one of the other releases.
Though lead flies aplenty from all manner of weaponry, and the scripted event sequences turn you into an action movie hero, this first-person shooter isn't all guns in the sun. Much of Predator requires a stealthy approach, and sends you creeping through bushes, setting nasty branch-whip traps, throwing rocks to divert attention and driving all over the back of beyond, all with intuitive and responsive controls.
The sound is also immersive, filled with indigenous birds and rustling leaves. It's not just for show, either. Tension rises with every snapped branch, because the bad guys are smart enough to investigate when they hear you crashing through the underbrush, instead of just deciding "it must've been the wind." But once they've found you, they still do some stupid things, like charging straight toward the barrel of your gun while getting hammered with bullets.
