I just got a Spigen NEO Hybrid EX Slim bumper case. (I have the Bodygaurdz PURE screen protector and a Zagg on the back and they work fine with this case.)
The case is very nice--with my black iPhone 5, the "Metal Slate" color looks very close to the phone's color and blends in well.
Is it thin? Yes, but not super thin like I'm looking for. It feels very nice but not as nice as the metal of a naked 5 or, perhaps, a metal bumper case.
The problems I've had are due to the bottom ports: I have a PROCLIP in my car with Lightening charging cable and I had to file away parts of the case's charge port and then color the marks with a gray Sharpie pen (yes, a bit OCD, thank you very much!). I also had to file and make the headphone jack bigger because my Westone earphones and my over-the-ear headphones have plugs with a base with a diameter that's too large. All are working now, however.
I'm still looking for a metal bumper that's very, very thin. There's a Kickstarter project claiming to fit my criteria and I've ordered one. If and when it becomes a reality, I'll let y'all know how well it works as far as THIN and FEELS CLOSE TO NAKED goes!