I'm not aware of any jurisdiction that has a law that explicitly states that a license notice must be included in each file, or conversely that it need not be included in each file.
In all countries that have ratified the Berne convention, all works are subject to copyright, whether they include a copyright notice or not. (A copyright notice may help, especially when seeking damages, but it is not required.) Absent a license, someone holding a legitimate copy of the work may deal with it in most ways (use it, modify it, etc.) but may not redistribute it. So if the license cannot be found, that's to the detriment of the recipient, not of the author.
The main risk if a file has no license notice is that the author A provides a user B with a complete multi-file work including a file stating the license terms, and B redistributes (lawfully, assuming an open source license) a single file to C without conveying the license terms to C. In this case, assuming a license that requires further distribution to be under the terms of the same license (which is the case for many open source licenses), C has not received a lawful copy of the work, since B's distribution to C would be a violation of the license. This is to the detriment of C, because they would then in principle not allowed to use the work in any way, lacking a lawful copy.
Including a reference to the license in each file makes it more likely that in such circumstances, C will be properly informed of the provenance and the license of the collection of files. It's a good idea, but there is no strict legal requirement.
Including a copyright notice in each file is also not required, since copyright is automatic as explained above. However it can be a good idea because a copyright notice can, in some cases, be circumstantial evidence of authorship and may allow the author to claim more damages in case of copyright violation.
One more bit that is often lumped with the license is a warranty disclaimer. That one's of a different nature, because unlike the bulk of the license, the warranty disclaimer protects the author. Warranty on works covered by copyright (such as software) is a bit of a strange beast — traditional law considers works covered by copyright to be artistic, not functional, and thus not subject to warranties. I'm not aware of jurisprudence regarding warranty statements on software, but it'll have to happen sooner or later. It's not even clear that typical warranty statements on software (whether open source or not) have any legal effect. However, if in doubt, this is one that you should include, since it protects the author if it's at all valid.