So many free software projects have beautiful art, specially websites, that I wonder where the coders meet their artists. Is there some place to ask for this besides the local art majors' schoolboard? I thought of IRC, but I fear that one might actually bother the small and frequent userbase by asking it there.
Well if your project is interesting enough, you are going to have a lot of artwork. The problem would be to choose what suits you. I mean icons, logos and such.
Not quite sure about css and other web things, though.
So I would contact people contributing art to opensource projects and hobbyist designers at deviantart or openDesktop.org *-look.org chain (I mean box-look.org, kde-look.org, you-say-what-look.org, these all are run by openDesktop.org)
Clarification after Mark Trapp's edit: if your project has a website, you can ask people to submit their artwork there. If you are a member of Linux users community of some sort, check out artworks section on its forums if there is one. Contact artists there or start a topic on your project. If you like someone's artwork, ask for permission to use it in your project.
As an example, I made up a sort of fvwm configuration, which would use a dozen of .xpm files to render window decorations, but I'm not a good artist at all. So I asked for permission from one guy making openbox themes to use his artworks and I got it. Than I made one more set of pictures myself, and now there are two more guys who learned about my configuration from Linux community forum and thought it was good for them and who are better with graphics editor than I am. They made up several more sets of .xpms and color schemes for themselves, but now all of us can use them as they are or modify them. And it was not difficult at all even for single person.
Speaking of projects - take a look at Linux Mint forums - see how many artwork volunteers would propose.
When you run even a small open source project, you normally contact people, and some of them are willing to help you for some reason - they might contribute some code or some artwork, just let them know they are welcome to do so. Of course you'll have to polish it all yourself to make it fit into your project, but you'll get some material to work with.
Definitely some part of artwork would be of bad quality, like all that nude girls or fancy cars ubuntu wallpapers. But someone might contribute something as awesome as faenza iconset.
This is not the entire answer, but there are resources such as icons and clip art in the public domain that are free to use. I use the KDE crystal icons in one of my applications.
Have a look at: http://www.openclipart.org/
As far as websites are concerned you can use freecsstemplates.org as a starting point. With not so much effort (just need to provide one or two photos) you can get a pretty neat look. If you do a search for "free web templates" you'll see that there is a lot of simiilar places to get your website started.