It kinda slightly saddens me that I am to be the first to say this, but it was most certainly Mechwarrior 2. The explosions and robots drew me in, but what really captured me was that strange feeling of solitude you got running through a mission alone, destroying your enemies with brutal efficiency as you did your duty as warrior of the clan. It's a feel that no other game, not even the expansions, were really able to capture.
After that, Runescape, Age of Empires II, Pokemon, and finally Mechwarrior 4 all had a huge influence on my lifestyle, nay, my identity as a gamer throughout my childhood.
Any other 'mech fans around here?