As Andrew Wright says, "any" is followed by either a plural noun or an "uncountable" (non-count) noun. All of the examples that Richard London gave are non-count nouns, which is why they are not plural.
Some nouns can be either countable or uncountable, depending on the context. For example:
"Do you have any INTEREST in history?" (uncountable)
"Do you and your brother have any INTERESTS in common?" (countable, plural)