1. Digi Connect ME
55 mhz CPU
The company that makes this has other models, but this one wins on ridiculous factor; it's like a pack of gum with a 2.4ghz antenna coming out of it.
The family of products has support for Linux, Windows CE, and something I've never heard of.
2. Jack PC
Don't lie; you've had dreams of thin clients around your house. If keeping that small box bothered you, this PC is for you. It runs Windows CE, and they're looking into making a Linux distro (advanced users can probably make one, already). It has support for a few thin client standards (Citrix's and Microsoft's), though I'm sure Linux hackers could get LTSP and X going on it. The HDMI version even supports dual monitors.
175MHz MIPS CPU
Looking to borrow all your neighbors' WiFi at once? RouterBOARD has the board for you (and many others). They offer boards of varying size, CPU architecture (some are PPC), with different slots (mini PCI, PCI, compact flash), and price. Some even have daughterboards that add even more slots.
Some boards support Linux, and all support their proprietary RouterOS. Basically, you're getting a general purpose version of what Linksys and Netgear sell. You're paying a bit more, but getting a few more features, too.
266 mhz CPU
256 mb RAM
Compact flash slot for storage
My first dedicated router was a Soekris box. It's biggest selling point is a 586CPU, so any i586 is supported. I've heard stories of Windows being loaded, but no recent versions (i586, remember?), and the PCI slot doesn't supply enough power for a fancy video card.
It doesn't officially support OSes, but it runs most Linux/Unix variants.
6. Mini ITX
RAM supplied by user
IDE/SATA storage provided by user
These days, Mini ITX is hardly new, but if you need an almost full featured computer in a small form, and you don't want things to get complicated, this is where you look. VIA is the primary manufacturer, and their EPIA product line has almost any feature you're looking for. This is also the smallest board that has video, and the smallest aimed at consumers.
Consumers, be damned! Single board compters have been around forever, but not for consumers. They're as big as a full length (remember those?) PCI card, and come with slots for RAM, a CPU, IDE/SATA, and connect to a PCI bus and backplane. Backplanes can give you just a few PCI slots or a whole army of them. There are even backplanes designed for multiple SBCs, so a single rackmount case can hold 4 standard computers.
It's a standard motherboard in an unusual form, so any AMD64/x86 (there are probably IA64 SBCs, too) OS is supported.
After adding the wall jack computer, I felt bad for leaving this little guy out. Granted, it isn't really a computer, but if you need a few more ports in your wall and want it to look clean, it's perfect. It gets power with power over ethernet. Other than that, it's a simple 10/100mbps switch. Since it replaces a jack with keystone modules, they left space for two phone jacks (or other pass through connectors).