A large percentage. However, a surprisingly high number of my friends are rocking their phones without a case lately. It makes me nervous considering how fragile they are, but I think there's some appeal to going caseless, though I'm not sure what it is.
Perhaps it's easier to slide into your pocket?
Or maybe it's more about letting everyone know that you have the latest phone? Who knows.
For myself, I go caseless because, 1) I like the feel of a solid metal device in my hand over plastic or rubber, and 2) it's thinner without a case, and easier to handle.
I have a leather wallet case that the phone slides into easily for when its in my pocket, as I wouldn't want it to get damaged being jostled around, but it's quick to take out when I want to use it.
My $99 Android phone (out-of-pocket, no contract) that looks nice (to me at least), has 6.0.1, and serves all my phone needs quite nicely has no case. If I drop it, it'll probably be cheaper at this point to replace it. Actually, I have dropped it a few times with no damage. I could care less about the thing at this point, even though it is easily the best phone I've ever owned.
I tried to go caseless, but thin metal smartphones are way too slippery. Every time I set my phone down on something, it always seemed to have some velocity towards the floor, just a matter of time.
Also, it feels wrong setting the iPhone down on a bar table or whatever. Either the touchscreen lays against the table or it's seesawing on its protruding camera lens.
Putting it in a minimal rubber case took an $800 load off my mind for $15.
Perhaps it's easier to slide into your pocket?
Or maybe it's more about letting everyone know that you have the latest phone? Who knows.