I don't think that you could simply remove a single game from my history, introduce it to me today and have it have the same effect. That said, I believe the question is similar to asking: For which games do you have the fondest memories? For me that would be something like:

Duke 3D
Donkey Kong Country
Goldeneye
GTA 1
F/A-18 Hornet 3.0
Half-Life/CS/TFC
Asheron's Call
Street Fighter III: 3rd Strike
Gran Turismo 3
Guild Wars 1
Battlefield 3
Farcry 3

As somebody says, some games are too old to have the same kind of impact today. I suspect that the person who originally came up with this question may be somewhat younger, at least enough so as to not be too subject to this issue as much. But let's imagine I could play it again and it would have the same impact it did back then... If so, I think for me, it would be a draw between:

Under a Killing Moon

and

Command and Conquer II - Red Alert