You can pack your own boxes however boxes packed by the owner may not be covered by insurance. Whilst it may appear that you are saving money if you pack yourself, in the long run this may be false economy.
Post 9/11, Customs requirements in every country have strengthened and packed by owner personal effects come under high scruitiny that could eventuate in Customs examination and inspection fees not included in your quotation. Some countries such as the USA and Canada do not look favourably upon boxes that are packed by owner and will undertake extensive examination at your cost.
If you would like to pack yourself, you can purchase cartons directly from Overseas Packers & Shippers.
Please note: boxes packed by a removals company often move through customs more quickly than those packed by the owner.