I've tried a bunch of them out, most recently the Urban Armor gear case. I'm generally not a fan of cases for anything unless they provide some measurable benefit (iPhone 6 has a Surface Pad on it, and my Note 4 has a Seidio case on it). I've never put a case on any laptops, but with my SP3 I almost feel like I should.
For the most part, mine is naked except I have a Type Cover for it (and honestly, I'd love to get rid of the Type Cover as I use an external BT keyboard from Lenovo that I love). And like others above, I love how slim the SP3 is.
That being said, I've had the UAG case on it for the past couple of days, and I do like the "grippiness" of the case, though I'm not the biggest fan of the stand (it's okay....just not as good as the built-in kickstand). But it does make it bulky, so I'm currently debating whether to return the UAG to the MS store.
I bought this Asuxtek slim case for mine, and I don't like it. It completely defeats the SP3 kickstand, and it's not reliable enough as a stand itself. Otherwise it IS nice and slim and protects it well. If anyone locally in the Toronto area wants it, they can have it (free, as in beer).
http://www.amazon.ca/gp/product/B00KRTQS5K?psc=1&redirect=true&ref_=oh_aui_detailpage_o02_s00
I have an Armorsuit set of body protectors on order for it....maybe that may ease my paranoia about damaging it (though I also have MS Complete for it...but the fact that you still need to re-install EVERYTHING in the classic Windows Desktop environment is a horrendous PITA).
Patrick