Note: This essay was/is being written in response to a common argument (and counter-argument) heard on deletion requests. Feel free to edit it like it wasn't in a userspace.
Phrases like "there's no proof that this is PD/GFDL/CC/self-made/etc." and "there's no proof that it isn't" are commonly heard on deletion request discussions. Who's right and is this even a valid argument?
On Commons, it is the uploader's job to provide proof that the file is not a copyright violation—not the other way around. Some might say this runs counter to "assuming good faith" because it's as if saying "we don't trust you, give us proof!", but this is the same as Wikipedia's verifiability policy. It is crucial and defining to our project's purpose and function. (Besides, we assume good faith by allowing uploads before the proof.) Unlike other file repositories, we don't wait for notification of copyvios to take down images where we can help it. We can not allow images unless we know for sure they are free. Yes, in some cases, this may seem a little more restrictive than is necessary, but we do this for three reasons. We respect artists by not infringing on their rights. We respect the law by following it. And most importantly, we respect the free/wiki community by making damn sure our content can be used freely. This is the whole purpose of Commons—to be a free media repository.
How do you "prove" it?
In most cases, a link to the source is all that's needed to confirm the license. Sometimes permission or a clarification is needed from the copyright holder. This can be done by e-mail (here's some templates to start with). This exchange (both request and response) needs to be forwarded to OTRS for confirmation.
There are many resources and fellow Wikimedians out there to help you. This page is neither.
What if the uploader doesn't know or forgets to add this "proof"?
One of two things must happen. Either the necessary information will be added to the image's page or the file will be deleted. Usually, the latter.
For the most part it happens naturally, but it should be said that the more valuable a given image is, the more time and effort should be spent determining the copyright status. If you see a potentially valuable image that is missing this essential information, you should try and provide it instead of simply nominating it for deletion. If you can't find this information or are unclear about it, then nominate it. This will bring it to the attention of others who can give it a try.
When the uploader fails to give enough proof, it becomes the community's duty to help "save" the images. However, some images just aren't worth the time. As Commons, we have what may seem like a endless supply of unsourced files but we don't have the human resources to match. We need to focus our energy on things that are truly important. High quality, rare, unique, useful, educational images and, of course, images being used by Wikimedia projects should receive extra attention.
What if you can't prove it?
Sometimes it's difficult, even impossible, to prove an image's copyright status. This is not the same as "knowing" the status. If the copyright is completely interminable (as with some anonymous works), we can not keep the image because there's no way of ever knowing if it's allowed or not. However, "proving" the copyright is different issue—the copyright can be determined given the necessary sources, though sometimes the "proof" itself is unclear and warrants further community discussion.
A question is what if this "proof" is off-line? (For example, if the uploader scanned the image from a book.) In cases like this, we should generally assume good faith and trust the uploader. (Now this is assuming so it shouldn't be done if you have good reason to believe otherwise, e.g. the user uploaded images in the past that were mis-licensed.) If we don't trust these uploaders we will be missing out of a lot of images that are not online. These files have extra weight because of the fact that they are not online elsewhere. They are harder to obtain and deleting them would make them a lot less accessible to a lot of people. Being the first resource to provide these files to the Internet at large is an honor and strengthens our role and impact on the whole wiki community.
Quite possibly, the hardest to prove copyright status is when you yourself are the copyright holder and Commons is the only place where the work has been "published". In other words, we have to take your word for it. Unless there is reason to doubt you, this is enough. We should keep the image unless there is proof of a copyright violation. If the work has been previously published (like on your own website) then you must either place a statement on the site declaring the "free use" license (usually in the form of a copyright notice on the bottom of the page) or send the permission directly to OTRS.