It depends on the height between me, my destination, and my previous spot. If I am at a place where falling down will mean the death of me, I will at least put my hands on railing. This had never happened to me before, however. I usually do place my hands on the rail on an escalator. It could be out of laziness. Out of those situations, I can't think of anything else in mind.
Things aren't so much different when it involve the rails in one's household. I have a steady balance of myself, and I not foolish enough to go up the stairs with somoene on it. That would only mean that the both of us would have to move. During that moment, anything could of happened that would place us in a dangerous position. Someone could've tripped and fell on the other, or a person might have been hit by a body part of the other person and are tumbling down the stairs. Stuff like this happened before; I've seen many people fell down the stairs because the aforementioned reasons. That, or someone might have pushed someone by accident or on purpose.
I've never fell down someone else's stairs before. So, I guess I'm too reluctant to use a rail as well. No one had ever pushed me off before, nor had I been in a collision with someone else. My fear of heights won't come to effect when I'm only a few feet off the earth. I also didn't take to account how dirty the rails are. It's been outside since the day it was made till the day it erodes. Between that time, the rails would get dirtied by rain, dust, bird dropping, pollin, etc. In my opinion, sometimes, putting your hands on the railing is not such a good idea. Well, at least clean your hands after.