In a 'bum bag', ie.. I carry it around my waist, covered up by a t-shirt. In my experience, it's certainly the safest way to carry it!
Unfortunately there are far too many scroungers out there waiting for a victim to pass by them in a foreign country and not aware of the dangers that are around them. At least if it's carefully concealed and not left lying around, it's harder to get hold of!
All valuables such as cash, travellers cheques should be kept as close as possible to the individual. I usually keep my valuables in my purse or a waist pouch.
I keep it on me. I usually try to only have a few dollars in cash, then use my card for larger purchases if needed. I double check every time I go to a new place to make sure I have my things. I've been known to leave some thing behind every now and then.