For me it was Unreal Tournament '99. It wasn't the first FPS I played - that was probably Doom '93 - but UT99 was the first one which really grabbed my attention. The fact it was running on a uni friend's then high-end PC helped since it was the best looking FPS game I had seen :-)
Your welcome, glad to be of service :-)
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Quake II way back when. I got hooked and then bought the extra mission packs. In fact, I still have the CDs.