Is there a reward for completing XCOM without any casualties (KIA)?
I did this on one of my Easy runthroughs of the game, and there's nothing in particular that happens. There's no associated achievement, either.
There is a post-game statistics screen that compares your performance to the statistics of others, where you can feel proud about your accomplishment, however.
I've finished the game without getting any soldiers killed (required some reloading). As stated above, there is no benefit for doing this other than personal satisfaction. Also, if you want to make sure no soldiers die, don't play the tutorial. Three soldiers will always die on the first tutorial mission and they'll show up on your memorial wall.