Lord Chesterfield: Letters to his Son, Oct. 16, 1747.
"Women have, in general, but one object, which is their beauty; upon which scarce any flattery is too gross for them. Nature has hardly formed a woman ugly enough to be insensible to flattery upon her person: if her face is so shocking that she must in some degree be conscious of it, her figure and her air, she trusts, make ample amends for it. If her figure is deformed, her face, she thinks, counterbalances it. If they are both bad, she comforts herself that she has graces; a certain manner; a je ne sais quoi, still more engaging than beauty. This truth is evident from the studied dress of the ugliest women in the world. An undoubted, uncontested, conscious beauty is, of all women, the least sensible of flattery upon that head: she knows it is her due, and is therefore obliged to nobody for giving it her. She must be flattered upon her understanding; which, though she may possibly not doubt of herself, yet she suspects that men may distrust."


Interesting how much insight this guy had over 250 year ago as he tried to relate his life's experiences to his bastard son who was away at school.
What's he saying here?
Basically don't tell a beautiful woman she is beautiful; she already knows it and assumes you and everyone else knows it. Figure out what her insecurity is and compliment her on that. Tell her she is smart, insigtful, interesting, whatever. In that way you'll stand out in her mind as being different.
In the same theory, don't tell an ugly woman she's beautiful. She can look in a mirror and know that she isn't and will know that you, like all the others is just trying to bullshit her. Figure out what she perceives counterbalances her ugliness and compliment her about that. You'll stand out in her mind as being insightful enough to see the same positive traits that she sees.
When do you tell a woman she is beautiful? When you can sense that she believes she might be beautiful, but is insecure in that belief.
Such advice has been quite helpful in dealing with strippers in the past. Some may think I'm certifyable for even bringing it up ;-)