Drakan: Order of the Flame is an action-adventure game that gives you the opportunity to take flight on a dragon and having him move and fight freely through, for the time, very detailed environments. This alone is a level of awesome, few games have achieved since!
This actually was one of my first video games. I remember playing it on my parents' PC together with my little sister, taking turns after each death. For some of the platforming in the early parts of the game, we even shared controls, one controlling the camera and movement, while the other timed jumps and rolls.
The movement of Arokh felt wonderful and even though the levels are quite linear for the most part the flying gave me a feeling of freedom that wasn't comparable to anything of it's time.
The characters of Rynn and especially Arokh are another strong point of this one, and I can still quote some of the dialogue all these years later.
My username clearly reflects that the Game stuck with me and even now I like to think back to one of the more unique action games of all time.
I'd say that this is in the Top 3 of most influential games for me and it would be awesome to experience it again on a modern system.