Shortcut: COM:FAIRUSE · COM:FU · COM:FAIR
"Fair use" not allowed on Commons
Wikimedia Commons does not accept fair use media files (such as non-free logos, covers, screenshots, or reproductions of other copyrighted works) because fair use laws vary from country to country—thus, content deemed acceptable under, for instance, US fair use concepts is not usable in the majority of other countries.
Fair use depends on the context the image (or other media) is used in. That is, something that can be used on one page as fair use would be a copyright violation on another page. Also, fair use does not allow for the storage of material on a general media database such as Commons. This means that fair use concepts simply do not apply on Commons.
Both issues are against the Commons policy of attempting to provide media files that can be used by anyone, anywhere, for any purpose. The Licensing resolution of the Wikimedia Foundation (WMF) explicitly forbids Commons to host fair use materials.
"Fair use" allowed on some Wikimedia projects
You may, however, submit such images to your local wiki, if it allows fair use. Note that files uploaded to a local wiki can be used only locally at that wiki.
Some, but by no means all, local WMF wikis allow the uploading of certain non-free material under very limited conditions, provided they have adopted what the WMF calls an Exemption Doctrine Policy. You can check whether your local wiki has adopted such a policy here.
The Dutch Wikipedia, for example, does not allow keeping any local files. Any files that are uploaded are moved to Commons or deleted. The English Wikipedia, on the other hand, does allow fair use materials subject to its strict non-free content policy, which requires the uploader to provide a detailed fair use rationale. The restrictions on Fair Use placed on editors by Wikimedia policies and guidelines, are stricter than those imposed by the laws of the United States.
If your local wiki does not allow the uploading of fair use material (and some, such as Spanish Wikipedia do not allow local uploading at all, making use only of media on Commons), then on that wiki there is no way of accessing any non-free or fair use file except through an external link (as hotlinking is disabled on Wikimedia wikis). If you are unable to persuade your local wiki community to adopt an Exemption Doctrine Policy then there is no option but to try to find replacement files that are free.