Hmm... if we're counting games where you can play in either 1st or 3rd person view, then I'd go with Vampire the Masquerade: Bloodlines. It's my second favorite game of all time (after Fallout 2), so that's a no brainer for me.
If we're talking games that are exclusively 1st person, then... maybe Dark Forces? I played that game an obscene amount when I was little. Runners up would probably be Daggerfall, Deus Ex (the original), and Golden Eye for the N64, which I also played a lot as a kid. Strangely, I haven't played many exclusively first person games in recent years.