I Say Hiccup

Hiccough and hiccup are both correct. Certain people will favor one form over the other. For me, I generally think of writing it as hiccough. Hiccup may be the older of the two spellings, but either one should be understood. Just try to be consistent when using it in written form.

Hiccup

I would write and say "hiccup." "Hiccough" is pronounced the same way as "hiccup," but it looks more old fashioned.