How many folks out there shoot with a single shot rifle or shotgun, exclusively?
and/or actually prefer this style of gun?

I do.
My Encore and NEF has always gotten the job done for me.

For 22 caliber plinging, I prefer the single shot as you don't burn a box of ammo quite so fast.

I have a 22, and 20 gauge both single shot but i would rather have a semi or lever action 22 for plinking, but it is an accurate little thing so i cant complain, the 20 gauge served me well until i switched to a 12 guage for bird hunting.

I have a bunch of muzzleloaders. Does that count?

I have old pokestalks from when I was a kid but graduated to the "be prepared for that next shot mentality". Never use them now. Single shots don't work well on duck and goose, I have found. I wouldn't mind to have an encore in muzzleloader and varmits

I am hooked on my NEF rifles and shotgun. I do not however use them only. I could though if I could get a few more calibers in the NEF. I have a couple Stevens Little Favorite 22 single shot rifles. They are fun to shoot as well. I could hunt everything in NA with my NEF 45-70.

For me, i have no problem hunting with a single shot rifle. Hunting big game with a single shot, makes you take your time and do it right with the first shot!!

Although i own numerous repeating rifles, i don't have any that i like better than my old drilling!! Over the years i've owned it, it's put a "lot" of both big and small game animials in my freezer!

Drilling Man

For hunting, its Contenders and Encores only!! Calibers from 22lr to 45-70.

I love my Ruger #1 in 7 STW with a Simmons Aetec.

The only single shot I got is my Bow. And I love shooting it.

I actually prefere the single-shot rifle, and double shotguns (SXS!!). I am also partial to muzzleloaders! But I do still have a couple of bolt-action rifles. I actually shoot these once ion a while, still. I do like double rifles and DB ML rifles like the Pedersoli Kodiaks.