I've never walked down a hill on my road bike or touring bike, but I have on my mountain bike. I'm not a very technical rider on my mountain bike and steep switchbacks with cliffs scare me, but on the road, I love to go fast and do quite often. I was on a ride today and hit a nice downhill that got me up to 50mph.
The biggest and longest descent I've done was on a ride from Walden, Colorado to Fort Collins, Colorado. After you go over Cameron Pass at about 10,200 feet in elevation, you descend for about 65 miles and drop about 5,200 feet in elevation. Not that steep, but a beautiful and fun descent through Poudre Canyon.
Those pictures that acantor showed are beautiful and I could see having to walk some of that because the cobblestone road would probably beat the heck out of you.
My touring bike has disc brakes so I don't have to worry about over heating the rims and it takes less pressure on the brake handles so my hands don't get tired. My hands have definitely gotten tired on my road bike going down a steep hill with lots of switchbacks.