Well, there's the Blue Ridge Parkway - what else can you ask for??? Seriously, North Carolina is a paradise for driving entusiasts. As a whole, the drives on the western part of the state are superior to anything this side of the Mississippi. I haven't fully explored all the snaking roads that are draped across this state's many backs but what I've seen always leaves me wanting for more pic1 and pic2.
The Blue Ridge itself offers the most rounded package in that it's a tourist road. As far as I can see it serves no significant transportation purpose; it avoids metropolitan areas, provides only minimal connections to other roads and instead carves paths across the mountains to exploit the most from the scenery. And the road itself has another couple major points going for it 1) it's kept in immaculate shape. Not just the tar job but they go the extra mile and keep the grass shoulders jealously manicured and, 2) the roads are relatively free of cars even on busy weekends. Expect plenty of curves, downhills and uphills. I can't think of a single thing to whine about this great road other than it's fairly out of the way of major cities.
Want something a little more off the beaten path? A little less civilized perhaps? Then consider the Cherohala Scenic Skyway (rt. 143) which is directly south of the Great Smoky Mountains National Park. Half of it lies in NC and the other half in Tennessee. The carolina portion is the funner (and more scenic) drive of the two and provides the lion's share of the mountain road goodness. The many small, yellow speed limits are conservatively rated and my guess is they're there to prevent mini-van drivers from having a little *too* much fun. For the rest of us, however, they can be, um, "experimented" with. Generally I found they can be taken at roughly twice the posted speed. Of course, the disclaimer applies that you should be paying close attention to what you're doing, that you're a halfway competent driver and that your gear is up to par. The Tennessee side dispenses with much of the high-altitude open-air scenery for thick forests. So thick, in fact, that the brightest day can't overcome its dominating shadows.
Way down the fun-to-drive scale but still worth doing (if for no other reason than because it's easy to get to) would be the I40 segment from Asheville to Knoxville riding the Appalachian hump. The road is suitably curvy and hilly for a good soul workout but, this being a primary east-west vein and all, the traffic can become a nuisance. Thankfully, the roads are kept well and I've never seen any cops in the area.
I'm much less enthusiastic about eastern North Carolina pic 3 pic 4. Mostly because it's flat and its roads utilitarian. Flat roads elicit heavy footed gas pedal treatment though and, if this is appealing to you, there's probably no better, straighter road than the stretch of I40 from Raleigh all the way to Wilmington on the coast. Again, however, the self-evident cautionary note of picking a non-peak travel time is crucial to avoid heavy traffic pic 5.
I was also hoping to speak highly of the drive on the Outer Banks area but instead found it to be a tourist trap. That means killjoy road restrictions, non-scenic drives (the road from Nags Head to Ocracoke runs its entire length straight down the middle - hardly a wink of the ocean on either side can be seen while driving). Still, I don't regret having gone because the area is charming notwithstanding its lack of driving appeal.