Depends on which astronomer's catalogue you go by.

There is a Bright Star catalogue, which lists all stars visible with the naked eye. It has 9110 entries.

http://www.alcyone.de/SIT/bsc/

Here is the Wikipedia entry on star catalogues, which lists different ones.

http://en.wikipedia.org/wiki/Star_catalogue

However, you could just make up a reasonably high number.

I believe there's a hero in all of us that keeps us honest, gives us strength, makes us noble, and finally allows us to die with pride, even though sometimes we have to be steady and give up the thing we want the most. Even our dreams. -- Aunt May, Spider-Man 2