I'm with Greedyfly - when strangers sneeze, especially if it's more than once, I get really irritated, which is irrational.
My other handkerchief-related peeves are -
men who sneeze and never carry a hankie or a tissue - what's wrong with you, you're a grown-up for God's sake!
(usually) women who blow their noses, and then peep into their hankie - what, do you think you've got pound coins up your nose? Stop it!
Oddly enough, the present Mrs Hughes never ever sneezes just once, it's a minimum of at least three, usually five times, and that doesn't irritate me in the slightest, because I love her.