My own view, which is at the extreme end of the spectrum I know, and therefore not (yet) formal policy in every case, is that we ought to have almost no fair use, outside of a very narrow class of images that are of unique historical importance. The cover of an album is the best and only sensible illustration of an article about that album, for example. A screenshot from a movie is often also the best and only sensible illustration. Some pictures (Elian Gonzales and the Border Patrol for example) are historically critical and irreplacable and worth fighting a fair use battle for if necessary. But an ordinary photo of a random celebrity? We are much better off to have no photo than to have a fair use or even "wikipedia only" photo.
—Wikipedia founder Jimmy Wales 
Wikipedia is, and always has been, a project to create a free encyclopedia; not free as in no cost (though it happens to be that too), but free as in unencumbered by restrictions. You can copy Wikipedia content and modify it in any way, or even charge for it if you like, and the only obligation you have is to allow others to do the same. This is the nature of free copyleft licenses like the GNU Free Documentation License, which Wikipedia is licensed under; they use the copyright system to guarantee freedoms, rather than restrict them. It ensures that Wikipedia content will always be accessible and usable to as many people as possible, and not tied to the whims or fortunes of any one entity.
Text contributions to Wikipedia are automatically licensed under the GFDL. These are the terms you agree to when you click submit and there is no going back after that. Images, on the other hand, carry a wide variety of licenses. Many of them are released under free licenses such as the GFDL, and many of them were released into the public domain by their creators. A significant number, though, are fully copyrighted and are used under the doctrine of fair use.
Fair use is fine for album covers, when our only alternative is to have no image at all. However, already having a copyrighted photograph of a celebrity discourages people from producing a freely-licensed one and uploading it. The end result is rather than having a more comprehensive free work, we have a lesser one accompanied by a copyrighted image that in many instances is unusable.
There are usually alternatives to fair use. Instead of copying an image of your favorite movie star from another web site and uploading it as fair use, pay a professional photographer for the copyright to one of his photographs and then release it under a free license. Alternatively, carry your camera with you next time you go to Los Angeles, California and see if you run into him Or better yet, find somebody else who already did that and request that they release the image under a free license. These may seem like longshots but the end result if this is applied project-wide is many more free images than we had before, and less fair use images that are not usable in many other settings (and thus the images won't be reusable by those who copy or fork Wikipedia content).
The Bottom Line: The goal of the Wikipedia project is not to amass a bunch of content at the wikipedia.org web site. It is to produce a free, portable encyclopedia that can be re-used by anyone, anywhere, in virtually any way. Using fair use images when we don't have to provides less motivation for users to upload free alternatives. We should only permit the usage of copyrighted, fair use images when there is no alternative possible, and actively forbid and eliminate the use of fair use images in other circumstances.