Some people travel internationally with valuable personal effects. The most obvious example is photography equipment which could easily be valued over $15k. Jewelry, watches, and specialized medical or sports equipment (think expensive bicycle) also seem likely expensive personal effects that people might travel with.
For most countries it seems that personal effects are not subject to duties (see also "Customs and Duties" of this answer). Of course, this depends on the customs official accepting your claim that the items you are importing are personal effects. If a customs official rejects your claim that they are, in fact, personal effects, it seems clear that you would have to pay duty on the items. While this seems uncommon, there are reasonably credible stories about travelers being charge import duties the personal items they are traveling with including this one about photographers returning to the USA and this one about a visitor to China's iPad.
How do I avoid being charged duty on my valuable personal effects when I cross a border?
This is probably one of those questions that will have a different answer for each country, so I've left it country-agnostic. I've found the answer for leaving and returning to the USA, but I really need an answer for traveling from Canada to Germany, Italy, France, Switzerland, and back to Canada via Germany.