In racing games Yes, the more realism the better. Especially damage, very important.
In FPS' it depends. In a REALISTIC FPS' one bullet, one down would be realistic. Not necessarily a kill, but if you get shot in your leg by a 7mm round, you are probably going to fall down and writhe in pain awhile.
So, no, I'm not down for realism like that. But, if you take away crosshairs, give me ironsights only and let me take 3-4 bullets before dying I'm down.
Also, no-hud would be good. Just integrate the HUD elements into the game, like press J to count ammunition, shows an animation of yourn dude checking his clips.
Or M for map, you pull out a map. Or O for objective and you pull out a piece of crumpled paper with some basic instructions.
I'm down for THAT kind of realism. But definitely not hyper realism, one bullet in the chest and you die type deal.