Although this discussion gives examples for U.S. customs processes, the basic precepts apply widely.
If you plan to travel to other countries, you don't want to risk paying duty (as you return) on items (especially valuables) you already own and take on your trip...even including engagement rings. As you return from any international trip, you can be charged duty on all valuables you have with you that exceed your duty exemption.
For fine jewelry, newer model cameras, electronics, computers, etc., your government's customs bureau likely offers a means to avoid the problem. As an example, U.S. citizens can go to the Customs web-site for a Form 4457 mentioned in their other pages under "Know Before You Go" . For most people anywhere, the steps essentially include...
Take whatever valuables you choose; just remember related customs forms on your international trips, and have them handy for Customs inspection as you return to your home country. Original store receipts from merchants in your country can be a fair substitute for proof of prior ownership if you lack time or access to a customs office before your trip. Even if dated well before your trip, receipts from sellers in other countries often have little standing.