Avoiding the traveller's 'fanny pack' / money-belt

There's another option which consist in the same bags you described but hidden under your arms: Undercover Body Safe bag I can also think that can be placed under the shirt or outside (like in the picture) if you have a jacket or so.

I think the decline in importance of cash is your friend here. If you mostly use cards (whether debit or credit, and they make debit cards that mimic credit cards so you can use them at places that don't take debit) then if a card is stolen, you cancel it and use a different one until your replacement arrives. As long as you don't keep all the cards together, you're ok. I typically head out for a day of sightseeing with two cards (one debit and one credit) and enough cash for coffee and a snack, perhaps double that. They're in a pocket or a purse and while I've never been relieved of them, it would be far less hassle than having hundreds or thousands in cash or travelers cheques taken. (That moneybelt picture shows 500 Euros. I would never wander around with that much. Why would anyone?)

I don't think the fanny pack is about security. More about quick access to things you use a lot. The only place I've ever worn one is on a portage trail, where they're just the right thing for the purpose. If anything, a bag like that is LESS secure than a pocket, since a knife to the strap behind your back lets someone run off with the whole bag.

My solution is to split money (and other valuable documents) between my luggage and my person. I find that zipped pockets in all my clothing allows me to distribute things on my person into a variety of secure(ish) pockets. My shirts, in addition to having breast pockets (useful for immediate cash and change) have a zipped pocket behind one of the breast pockets. My windshirt has a similar zipped pocket. My trousers have a variety of zipped pockets - some internal to other pockets. I have found it useful to store my passport in one of the front zipped pockets - I am constantly aware of its presence without having to check it all the time.

Any money or travel documents in my luggage will be buried, usually in dirty socks, deep in a stuff sac, that goes in the centre of my luggage.

This solution started out because I live on a boat and I was concerned about accidental loss of objects from pockets into the water. However, it has proved equally useful for travel - I know that it has foiled one attempt at pickpocketing whilst I have been travelling.