I strongly advise against fanny packs. I admit I personally find them unattractive, but they also are not keeping your money safe, which is what people think they do. I have lived in NYC for over 15 years, which has its share of pick pockets (although not as bad as many European cities) and believe wearing a fanny pack is like carrying a neon sign saying "I am a tourist please rob me". Also, although I have never had my pocket picked, my friend, in Paris, had her fanny pack deftly unzipped and her wallet lifted in the span of about 3 seconds. Never felt a thing. Professional pick pockets are just too good.
Personally I have a very small Coach bag that I wear slung across my body (over left shoulder, bag hanging on front right hip), that has a fold-over flap and a metal toggle closure. As it is small enough that I can barely get my hand in there, it makes it alot harder for pick pockets. In tight places I place my hand firmly on top of it.
It's also a good idea to keep some cash in a separate pocket.
My two cents, for what it's worth!