Traveling abroad. Where do you stash your passport/important items?

[sushijerk]

I have a fanny pack from high school but it blatantly screams "tourist". I considered getting a small traveling kit and keep it inside my backpack, but people tell me that this is not safe. I am going to Asia, where I guess pickpockets and such are more common than in Europe.

Should I invest in one of those pouches you strap to your body for my passport/cash? Is this overkill?