Quite a few actually, though not all of them required it. Though whether you consider them 'good' is a different story (personally, I could not get into HL1).
Duke Nukem 3D didn't need a mouse in the sense that like Doom, the character will automatically shoot in the Y-Axis (against floating/flying targets), but it's the first game that I recall with free look.
By association (modified Duke Nukem 3D engine), I am pretty sure that Shadow Warrior had it too. Ditto for Blood.
But those were all '2.5D' games, so I think Quake is the first to really make mouselook a requirement unless you count Descent (pre-dates Duke Nukem 3D), but it's a bit different from standard FPS.
I am pretty sure that all 'True 3D' FPS since Quake (and there are quite a few between Quake and HL) supported free look.
To answer the question, I use inverted mouse (well aware that I am a minority - everytime I lend my computer for someone to play, I always get some reaction related to the mouse control). I don't recall any FPS defaulting to that setting though, only flying games (where I picked the habit).