I have done so in all games since the mid-90s at least, I know for sure I played MW2 this way (can't remember if it could be changed or not) both with a mouse and with a 2-button joystick.
I was playing another game the other night that does not let you invert Y (World of Warships) and was struggling because after playing this way for so long, it is of course completely natural and to do the opposite is nearly impossible. Whenever I play another a new game this is one of the first things I look for in the controls.
The first "pure" FPS games I ever played online heavily were UT and Counterstrike (and later Source) and I remember most people played inverted back then but according to the people I used to play MWO (that have now moved on to Warships) with they think I am nuts and backwards. I figured this can't be the case--surely lots of old school guys are still around that learned to play that way when games were in their infancy and have never changed.
Edited by Kain Demos, 10 July 2015 - 10:26 AM.