A good question, to be sure, but my answer depends on the specifics.
First game I was "introduced" to? Pong.
First game that showed me the fun of video gaming? Super Mario Bros.
First game that truly hooked me on gaming and started my addiction? Half-Life
I was mildly into gaming through most of the last 80's and early 90's. Pong was the start with the old faux-wood tv box from the 70's. SMB was the start of my early console years, when I started to learn how fun games were and how much better they were with friends. However, it wasn't until Half-Life came along that I realized two things. First, the depth and variety available in PC gaming. Second, just how incredible video gaming could be.
So in a way, I had three major "firsts" in gaming.