I've seen pretty much every AKC breed and then some. That's what happens if you end up at enough dog shows, lol.
I see things like Canaan dogs a few times a month. Have met roughly 15 pyrsheps, 5 Cirneco dell'etna, Danish Swedish Farmdog, several mudi/croatians, lots of pumi, etc. Welsh sheepdogs are extremely rare in the US but I have met 5 that do dog sports around here. My trainer has one. My other trainer has a lacy, which aren't super common though I saw them a lot in Texas.
I guess the rarest would be some New Guinea Singing Dogs and I didn't even see them at a dog event!