I use as many free tools as possible, most of them are open source software available for download.
GIMP - A painting program similar in most respects to Photoshop, only it's free. It allows me to write my own brushes and other plug-ins.
Fireworks - Not free, but this part of the Macromedia Studio MX suite combines both vector and raster editing tools and renders very quickly. Also, it takes most of the plug-ins I write for GIMP, and vice versa. I want Santa Claus to bring me the newest version.
Inkscape - An incredibly powerful vector drawing program. Not easy to learn, but it's free and, like GIMP, there are a zillion developers all over the world working on it and adding features.
Freehand - Another member of the Macromedia Studio MX suite, this one is a dedicated vector drawing program with the best user interface of anything out there. When Adobe bought Macromedia they shut down Freehand product development, but it's still one of my more frequent axes.
Alchemy Mindworks - I've been buying home-grown software from these guys since 1991-ish. I have several titles: Graphic Workshop is for quick file conversions and some snappy filters. GIF Animation Workshop and PNG/MNG Animation Workshop are for making little dancing baloney web page animations.
Audacity - A free audio editing program. It's bare bones, but it's free and has lots of plug-ins. You can install an add-in that lets it take most VST sound plug-ins -- most of which are also free. It's a great audio editor for portable use on a laptop since it isn't loaded down with tons of unnecessary bells and whistles.
Cyberlink PowerDirector - Video editing software, not free but cheap.
Dreamweaver - Still nothing better for building web sites, especially for a designer. I still use the Studio MX version. Santa...?
Flip Video Camera - Just the best little art toy ever. Check out the first rough video I made complete on it here.
Make - Make magazine has been around for a long time, and it's the goto place for conceptual artists and electronic sculptors looking to cook up something amazing.
PrintingForLess.com - Really affordable, high quality online printing service. I send em everything from business cards to promotional brochures and announcement cards for shows. Use this Secret Code to get $25 off your first order: RP1CL8AGI
Dim Dim - Screen-sharing and remote meeting software. Mostly free, and it's incredibly cool.