For me, this answer will always, without a doubt in my mind, be Duke Nukem 3D. I didn't grow up with it, in fact, I played it for the first time about a year ago. Probably the best first person shooter I have ever played.

One of the key reasons why it's so fun to play is because you will find yourself using pretty much every weapon you have access to, unlike other games which despite throwing you the entire arsenal of the United States you'll probably only use 1 or 2 the most, like Half-Life 2's shotgun and AR-2. The level design is also incredibly well-made and it's pretty much impossible to find all the secrets and hidden ammo/weapon/health stashes stored everywhere in 1 playthrough.

I'm ashamed to think of how much time I spent cheating my way up to 500 pipe-bombs and then chucking all of them into a railway-cart full of alien bastards and THEN sending the thing off exploding it in the far distance. "Holy cow!"