"Any" may be used with singular or plural nouns.

I can cite the Cambride Dictionary as a source:

http://dictionary.cambridge.org/search/british/?q=any

http://dictionary.cambridge.org/grammar/british-grammar/any

The Oxford English Dictionary agrees:

http://www.oed.com/view/Entry/8973?redirectedFrom=any#eid

Use your example in a sentence. 
If you use "any" before a noun, it is singular.

So for your star example, the correct one is: We do not have any star.

'any' means anything.

For example:

Do you want any pens? 

Do you sell any erasers?

You're confused whether to use 's' or no 's'

As i said, any means anything. Anything = many type.

so, if you use 'any' . u must put 's' infront

(╥﹏╥)oh no...

anyway thank you all the same my friends, but this is what I worried when I wrote the discussion. I don't want to see big differece between your answers and I know you are all English native speakers.

i really have an American friend and he told me should use singular behind the word "any" at all. He was very confident and sure, to him, a person who enjoy correcting Chniese and English essays here so I don't understand if no singular is true then he will be wrong?

But most of the English speakers tell me I should use no singular.

And I know we change "some" into "any" for ask and negative,"some"+plural,if "any" still have this character,then will be clear.

And I have a Chinsee friend, he tell me:1与不可数或复数名词连用，用于否定句和疑问句。2与单数可数名词连用，表示“任一”.(plural and singular are both right)

Anybody else?

You can also put 's even if there's a noun,what you must look at is if it's singular for example "pen" or plural "pens".But it depends on the structure of the sentence.Correct me if I'm wrong.