Is there any legitimate free mining website? Are free mining websites paying or are they all scams?
Absolutely none. I've actually seen a lot of them recently that are offering 'multicoin mining' with guaranteed profit.
Why would anyone want to offer you free GH/s? Obviously, to get you interested in the idea and potentially get you investing into the ponzi scheme. They know that this is an effective yet extremely cheap way to lure people into their scam because of the fact that nobody will ever be able to cashout just from free hashing power earnings.
You're better off doing faucets than trying to get a withdrawal from free hashing power. Trust me, sooner or later you'll just be tempted into investing and lose all your money. If you don't then after a year you'll still not make enough to cover tx fees, that is if the scam doesn't shut down before a year.