It is always recommended that you insure your shipment(s), but the reality is that you need to consider the value of the goods, the cost of insurance, the risk involved, and any excess charges or restrictions that might apply.
If you are a business, and you are doing multiple transactions, then you should discuss this with your insurance broker who provides your other business insurance and check if your import or export transactions are included as well.
Failing that, you can get an individual policy for each shipment; but this will always work out more expensive than if your shipments are just part of your annual business insurance, or you have taken out an annual policy to cover your shipping.
For import shipments, you are responsible for insuring your shipments if they are ex works (EXW), FOB or CNF. If the shipment is CIF, then you should ask for your supplier to send you a copy of the insurance policy that covers each shipment.
For export consignments, theoretically the reverse is true. But, just consider your exposure.
A friend of mine is exporting containers on an FOB basis; so theoretically his customer is arranging for insurance on the goods. But once, one of his containers arrived at the destination, and the consignee rejected the goods (for whatever reason); so, the exporter was stuck with a container load of product (that he had already paid for) in another country, for which he then had to try to find another buyer (at a hugely discounted price) or have the cargo destroyed at his expense. So, even though the importer was technically responsible for insuring the goods, the end result is that by him not doing so, it cost him a small fortune. All of which could easily have been avoided had he insured the goods in the first place. Now, regardless of the terms of sale, this exporter insures all of his shipments.
Insurance of personal effects is something that comes up regularly. If you pack the cartons or container yourself, then you will only be able to insure your goods for total loss. Breakage or damage or theft will never be included in this case. International removalist companies may offer this as an option if you were to utilise their services on a door to door basis, but you should check.