Inkscape is a vector-illustration package that lets you output images in a variety of formats, including the open SVG standard that's gaining support in modern web browsers.
If GIMP is the opensource fraternity's Photoshop, Inkscape is its Adobe Illustrator.
It's capable of creating page layouts for print or screen as well as logos, buttons and banners. In fact, Inkscape is probably up to any drawing task you can think of.
The standard tools for creating vector images are all there: generic shapes and gradient fills for neophyte users, Bezier paths and intersection editing for more seasoned computer artists.
Inkscape is popular enough to have its own wiki. There you'll find a user manual, some basic tutorials and galleries full of Inkscape art.
OS X, Linux and Windows versions are available, though it's currently a bit buggy on Vista.
Alongside OpenOffice.org and GIMPShop, Inkscape is one of few open-source tools that are close to essential on any free software fan's system.