I will kill anyone I want to in a game. I generally play my characters as evil, and when I decide my character is evil I take it to a degree that would make Darth Vader raise an eyebrow (of course not really, most games are quite limited).
Children and pets? Yes, I will kill them. Sometimes just because they're there and I'm rampaging, but often I'll get mad at a certain character and genuinely desire to ruin their lives by taking everything they own and killing their whole family.
If I were to play a good character, that gets more complex as to what good really is and all that.
I think the thing is that when I'm playing a game in which roleplaying is a factor, I will let the character decide, as Inkidu stated. If my character is an evil bastard who would cut the nuts off a dying puppy just to make its owner cry then by god he will do it.
In games like Rockstar's skidmarks or Saints Row 2, well, those aren't real people and who cares if they're dead?
Edit: To qualify, I have actually found a couple games where there were people I wasn't keen on killing. Near the end of KOTOR, when you make the decision to be dark/light and the wookie/twi'lek combo (I believe? Correct me if wrong) rebel against you, I had trouble fighting them. It wasn't the outcome I wanted, but given my character's penchant for mass murder and their principles (puny mortals), it was necessary.