I am slightly concerned about this question and the way we are treating it:
It seems there is a lot of disagreement as to whether the question should be on or off topic because there are some local rules that specify some requirements for invoices. These local rules can be significant and sometimes strict, but regardless there is also a lot of room for a general answer which gives both a guide to the commonality between countries and an idea of what sorts of things may need to be asked of a local specialist.
My thinking is that such a question should be on topic, because expecting a fully complete answer in a topic like this gets you into "too localized" territory quickly. If we want to nitpick, the requirements of a Canadian freelancer to send an invoice to a Canadian customer are different than they are to send the invoice to a US customer. For example, there is no reason to send the tax registration numbers to a US customer, but you would have to send them to a Canadian customer. Similarly if you are in the UK, you would send your VAT number to a UK customer or a French customer but it would not be required to send it to a Canadian customer. The fact that the requirements end up specifically pertaining to not only the issuer of the invoice but the recipient make this extremely fact-bound.
What I would like to see is some tolerance for modestly overbroad questions, provided they can be summarized and pointers given as to likely trouble spots for local laws. Otherwise I am afraid such questions can't be reasonably asked because any question asked with sufficient specificity for a fully complete answer would be too localized.
Does this seem way off?