If you were on vacation in your car, which highway would have you salivating the most? Thinking of those with high-performance vehicles, but if the scenery is attention-getting too, that’s on topic.
California Hiway 1 between Monterey and San Luis Obispo for the win.
I don’t know if it counts as highway, but some of the roads around Spokane are breathtaking.
Route 1 through Saugus, MA can be interesting. It’s like a weak immitation of the Vegas Strip.
The Sydney-Newcastle Freeway between Berowra and Mount White.
In Arizona, US route 191 from Clifton/Morenci to Alpine.
Starting from the desert floor, rises up into the mountains and pines with lots of curves along the way.
This used to be US 666 but was re-numbered when the U.S. government dropped the U.S. route 66 designation leaving it an orphan. The states of Arizona and New Mexico wanted the route designation changed to, because of the relationship of the route number 666 to Christian lore. (Paraphrased from the Wikipedia article here: http://en.wikipedia.org/wiki/U.S._Route_491#Elimination_and_renumbering_of_US_666.)
Crowsnest Pass. Simply gorgeous.
I can’t remember if it’s White Pass (Hwy 12) or Chinook Pass (Hwy 410) over the Cascades but you go around a corner and BAM! Mt Ranier! Stunning.
Oh, and Hwy 310 behind Mount St. Helens. Dark mossy forests that suddenly open up into the haunting devastation of the 1980 eruption. It’s a very long drive but worth it. When we went we didn’t see one other person on that road or at the viewpoints.
And any highway in Alaska. 
Wow, first response - I opened the thread to say exactly that. 
UT12 from Torrey to Bryce Canyon in Utah.
UT24 from Torrey to Hansville in Utah.
UT95 from Hanksville to Blanding in Utah.
US550 from Ouray to Durango in Colorado.
All of these offer a sporting experience, though for me I much prefer a motorcycle to a car. If you slow your pace down a bit, the scenery will blow your mind: redrock desert on the first three routes, alpine forests and tundra on the last one.
Chief Joseph Highway/Beartooth Pass between Cody, Wyoming and Red Lodge, Montana.
Believe it or not, southwestern Wisconsin has some pretty interesting roads. Several years ago I plotted a route from Madison to Minneapolis; via the interstate it used to be 280 miles, and by sticking to an alphabet soup of scarcely traveled country roads, I stretched it out to about 400 miles of twisty bliss through beautiful farm country.
The Smoky Mountains have all kinds of great stuff. Deals Gap (“318 turns in 11 miles”), just SE of Knoxville, TN is too famous for its own good: it’s insanely crowded and can be downright dangerous on the weekends, as every idiot with a sportscar/sportbike and an attititude comes down there to run it. Less traveled (and less patrolled) is the stretch of NC28 just south of there, AKA “the Hellbender.” At first it’s just as twisty as the Gap, but later on it opens up into nice sweepers that can be enjoyed at a higher speed.
Cherohala Skyway between Robbinsville NC and Tellico Plains TN combines long sweepers with scenic vistas as it crosses over the 6K foot mark.
Trail Ridge Road through Rocky Mountain National Park. Lots of campers, so don’t count on a sporty pace through here; just take it easy and enjoy the breathtaking views as you cross the continental divide.
Loveland Pass, Colorado. This is the route for vehicles prohibited from the Eisenhower Tunnel on I-70, so occasionally you get a tanker truck climbing the grade, but there are plenty of passing opportunities, as well as great views for pretty much the entire route.
CO92 from Gunnison to Hotchkiss.
CO141 from Naturita to Whitewater.
UT128 from I-70 down to Moab. Stop halfway through for a view of the Fisher Towers rock formation. Kill your engine, get out and listen to the silence.
US14 through Bighorn National Forest in Wyoming. From Lovell to Dayton, and also the branch down to Shell.
Did I forget any?
What comes to mind is a stretch of highway from St Davids to Waterloo, Ontario. It would take three hours travelling through many southern Ontario towns with a history to get to my university and back home as opposed to one hour travelling the antiseptic super highways of the QEW and the 401. Time is a valuable asset, but twice a week I had to ponder which way I would go.
California Highway 120 across Tuolumne Meadows, over Tioga pass, and down to Mono Lake.
US Highway 302 as it passes through Crawford Notch, New Hampshire.
CO 50 from just south of Grand Junction to Delta. Not because of the view, although there are some nice ones.
I drove this a few years ago when it had been recently resurfaced. It is undulating, has long, long banked curves in both directions, and there’s nothing along the sides of the road. I’ve never been on a road before that made me want to drive 130 mph as bad as this one.