You can do this if your characters are always facing full-frontal or looking straight at the viewer. Of course, that kindof makes you look like a one trick pony and your drawings stale. You've got to mix it up a little if you do that.
However I will say this: For us 3D artists, we are ok with doing only half a body and copy-pasting it. Characters are modeled using the T-pose (arms stretched out, back straight, legs straight together), and truthfully we only NEED half the body to begin with when modeling in our programs. This is excellent for us, but for traditional artists, you're not going to be able to do this and put your characters into good poses (due to lack of foreshortening and perspective).
It's ok to do sometimes on things like eyes and...um... hm... don't know much else really. Maybe clothing bases or accessories that are on both sides of the body. Really though, even slight asymmetry is better.