Asus EeePC as a Router
It seems to me that the Asus EeePC (a $AU499 ultra-light laptop with only flash storage) would make a decent router.
Often full desktop PCs are used as routers because they run the most common software and have standard interfaces. There have been dedicated router devices with flash for a long time, but without the ability to connect a standard monitor and keyboard they were always more difficult to manage than general purpose PCs. Also dedicated routers have limited RAM and storage which often does not permit running a standard OS.
According to the best review I could find  EeePC has a minimum of 256M of RAM, a Celeron-M CPU (32bit Intel), and a minimum of 2G of flash storage. This hardware is more than adequate to run most server software that you might want to run (my current router/firewall/server has 192M of RAM). It could run a web server, a mail server, or any other general server stuff. It comes pre-loaded with a modified version of Debian so you get all the Debian software (which incidentally means more pre-packaged software than is available for any other distribution). Bigger versions are common, I believe that the $AU499 version has 512M of RAM and 4G of flash - I’m not sure that I could even obtain a lesser EeePC in Australia.
The up-side of flash is that it doesn’t take much power as having a low power device in whatever confined space ends up housing your router is a good thing (the EeePC is listed as using less than 20W no matter what the load and idling at as little as 14W) and that it doesn’t tend to break when dropped or have any moving parts to wear out. The down-side of flash is that a sufficient number of writes will destroy it.
Obviously swap is not a suitable use for a flash storage device. But a small mail server (suitable for the needs of a home or a small office) should be fine with it. Squid is commonly run on router devices, to run it on an EeePC I would be inclined to buy 1G USB flash device for the cache, then if Squid’s use destroyed the flash storage it would be easy to spend $20 and buy another.
The EeePC has three USB ports and a built-in Ethernet port. I believe that the minimum number of Ethernet ports for a firewall is three, this means either one for the uplink, one for the DMZ, and one for your LAN, or two for uplinks (with a redundant uplink) and one for the LAN. The three USB ports allow using two USB Ethernet devices to provide the minimum three Ethernet ports and one for USB flash storage.
One notable advantage of using a laptop as a server is the built-in UPS (the laptop battery). Many people have put old laptops into service as servers for this reason, but usually an old battery gives no more than about 30 minutes of power, while a new EeePC should be able to last for more than 3 hours without mains power. Using a second-hand laptop as a server is usually not viable in a corporate environment as laptops are all different. Repairing an old desktop PC is easy, repairing an old laptop is unreasonably difficult and often more expensive than replacing it. The low price of the EeePC makes it easily affordable (cheaper than some of the desktop machines that might be used for such a purpose) and the fact that it is purchased new at such a price means that you get warranty support etc.