“Certainly there are things worth believing. I believe in the brotherhood of man and in personal originality. But if you asked me to prove what I believe, I couldn't. You can spend your whole life trying to prove what you believe; you may hunt for reasons, but it will all be in vain. Yet our beliefs are like our existence; they are facts. If you don't yet know what to believe in, then try to learn what you feel and desire.”

Variant transcription from "Death of a Genius" in Life Magazine: "Certainly there are things worth believing. I believe in the brotherhood of man and the uniqueness of the individual. But if you ask me to prove what I believe, I can't. You know them to be true but you could spend a whole lifetime without being able to prove them. The mind can proceed only so far upon what it knows and can prove. There comes a point where the mind takes a leap—call it intuition or what you will—and comes out upon a higher plane of knowledge, but can never prove how it got there. All great discoveries have involved such a leap."
Unsourced variant: "The intellect has little to do on the road to discovery. There comes a leap in consciousness, call it intuition or what you will, and the solution comes to you and you do not know how or why. All great discoveries are made in this way." The earliest published version of this variant appears to be The Human Side of Scientists by Ralph Edward Oesper (1975), p. 58 http://books.google.com/books?id=-J0cAQAAIAAJ&q=%22solution+comes+to+you+and+you+do+not+know%22&dq=%22solution+comes+to+you+and+you+do+not+know%22&hl=en, but no source is provided, and the similarity to the "Life Magazine" quote above suggests it's likely a misquote.
Source: Attributed in posthumous publications, Einstein and the Poet (1983), p. 136