A very smart answer. I wouldn't mind being anonymously famous, in that people knew my name but didn't recognise me on the street. Not sure how possible that is in our current age though.
I heard a great story from one of my favourite film directors, Peter Weir. He was in a restaurant and got chatting to the waiter. The waiter asked what he did for a living, and when he told him he directed Picnic at Hanging Rock, Witness, Dead Poets Society, The Truman Show, etc, the waiter just laughed and didn't believe him. That's the kind of fame I could be happy with. :)