Handkerchiefs.
Seriously. We needed some, so off I go to buy a pack. It becomes apparent that the shop I went to doesn't sell them anymore. I go to the next shop, and the next. None sell them anymore. They all offer tissues with wan smiles. Over the past two months, I have literally been to every shop in my town (excepting only the aquarium place), and not one sells handkerchiefs.
When did this happen??? 
You know, I don't think I've ever actually seen a handkerchief without benefit of some recording material, such as film or television.
I have seen prettily embroidered hankerchiefs around Christmas, packaged for no muss/no fuss giving. They are thin little things, though, more for tucking in a breast pocket than blowing your nose.
I don't know how small your town is, but the only places we find them are menswear sections of department stores, or occasionally at Ross/TJ Maxx/Marshall's. Target will have them in gift boxes at Christmas sometimes, too.
We use them a lot, but we don't have a ton around at any given time.
Ladies' hankies? I've seen them a lot at antique and thrift stores, but I prefer larger, less fussy men's versions.