If a game allows aiming down the sights, I'll almost always do it. Even if it's a close-quarters firefight and I'm wielding some sort of shotgun, I'll take those extra .5 seconds to bring the sights up and make my shooting more accurate. This has caused many an online death when I should have just sprayed and prayed.
I used to do this in games like CoD until I realized just how much it was getting me killed. Playing something like Halo helps, in that most weapons don't have scopes and if they do, they're only for magnification and not for accuracy (obviously useful with sniper rifles or precise aim on distant targets, of course).
For a little while I found it amusing to run around in Modern Warfare 3 on 360 with one of the sniper rifles that instakilled with either a body-shot or head-shot, aiming where I expected people to be when I came around corners, and if I spotted someone there, I quickscoped and fired to avoid aim penalties, killing them. Of course, if they were somewhere else, I got gunned down before I could re-aim because they actually had crosshairs and automatic weapons, whereas I was trying to run and gun with a sniper rifle (I was getting kind of bored of the game by then, to be honest).
I saw most people play through the level cap multiple times. I made it halfway to the level cap, I think, before getting bored with the game.