Warioware Inc and MGS1
Wii sport & Nintendo land.
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Most recent? Probably Journey. Although I have to say the 2 from my gaming lifetime that stand out timelessly as so innovative that the whole world had the feelings you are describing are DooM in 1993 and GTA3 in 2001. They both changed what gaming is forever in everyone's eyes and minds. From a technological standpoint Quake 1 as well. Completely revolutionized and basically invented multiplayer coding that became the standard we now have as commonplace today.
Probably Skyward Sword's motion controls, or the 3D on the 3DS. Can't get any more innovative than that.
Mario Kart 8, the zero-gravity and colorful levels had me in awe.
Sorry but thats not innovation.
Most recently, I guess Minecraft Beta was innovative and new... though I don't play that anymore.
Probably shenmue... Early 2001 or so.