most influential Gaming Engines

[Riobux]

As unpopular as this answer may be, I'm going to go with Source because it led to a lot of mods being mad.

 

[Space Spoons]

I'm not sure what the formal title is, but Super Mario 64's engine. To the best of my recollection, it was one of the first console gaming engines to try for the fully three-dimensional graphics/movable camera combo that has today become the standard. It wouldn't be a few years yet before they got it completely right, but there's no denying that SM64's engine was a huge leap in the right direction.

 

[Cain_Zeros]

The Unreal engine. It's even used to make children's TV shows, or so I've heard.