Funny, I was thinking about this some time ago.
I would have to say that although it was not my first game, there was this one game that effected me greatly.
I never was an actual gamer, neither did I own any video-game systems. As a child, I was satisfied with playing games on the PC. It was mostly ported NES games or games made for MS DOS.
And then, I visited my friend and he showed me a game he had. It was probably 1998 or 1999, and I was around eleven years old. The game he played was unlike any I ever played. It had great graphics and gameplay (for the time period), nice sound effects and music, a complex storyline, and best of all, cool cinematic sequences after every level.
Guess which game it was?
It was Dune 2000.
Only around 5 years later I discovered the game was based on a novel, some more years later I discovered a movie and a miniseries were made about it, and only after watching the movies I finally decided to read the book.
The book is a cultural-philosophic tale unlike no other, but back when I saw the game I know nothing about it. It was the first RTS I ever saw and the idea of commanding an army in a sci-fi world I could only describe as "F*cking awesome".
Since then I fell in love with Tiberian Sun, Red Alert the other games by the great Westwood Studios. And then Westwood collapsed and the legend ended. But the inspiration DUNE 2000 gave me lives on in a novel I never take the time to write down.