For most people who check bags when flying, the $3400 of lost baggage coverage offered by airlines (by U.S. law) on domestic flights is enough to cover any loss or damage (keep those receipts when you buy anything expensive however, and fragile or other "valuable" items such as electronics are always excluded from coverage, so keep those in your carryon). But if your flight is to an international destination, even if it includes a domestic connecting portion, different compensation rules apply. For most international travel departing from the U.S., baggage liability is limited to approximately $9.07 (USD) per pound for checked baggage and $400 (USD) per passenger for unchecked baggage.

Different (slightly more generous) rules apply for travel from the European Community. But for almost all international travel, these protections won't cover your loss if you have expensive clothing or other items in your suitcase. That's why you might need to buy excess valuation from your airline when you check in for your flight. In addition to the airlines shown below, foreign-based (non-U.S.) airlines also offer excess valuation. Do a web search for airline + excess valuation or call your foreign-based carrier. Note that this is not "insurance"--but it is coverage in the case of loss and, in some cases, damage to your checked baggage and its contents.

In addition, many foreign carriers offer excess valuation, some for as little as 50 cents per $100 declared. Check with your airline when checking bags.