I've been using the Asus eeePC for the last month or so and have been very impressed.
The eee is a tiny laptop style computer that runs a customized version of Linux. If you take a traditional 14" display on a laptop and fold it in half, thats the rough size of the device. Keyboard and screen are both small, and take a little getting used to. I can type fairly easily on it but the keyboard is too large for Blackberry-style thumb typing and too small for traditional touch-typing. There is a built-in trackpad, but an external mouse like the Logitech VX Nano works much better. The screen is 7" and has a built-in webcam (at least on the model I have) The machine has 512mb of RAM, and 4 gigabytes of solid-state flash storage instead of a hard drive.
By default, the eee boots into a customized version of Xandros Linux. It is all point-and-click and very easy to use, you never see a command line (unless you want to, more on that...) Preinstalled are Firefox with flash support, a mail client, Skype, and the Pidgin instant messenger program. Also installed is the Open Office suite, and all applications are easily accessed through a tab-based interface.
There is also an "advanced mode" which loads a customized KDE desktop and has a more customizable start menu interface along with a more traditional desktop environment. There are also instructions for installing Windows XP, but I haven't tried it yet. The machine boots up very quickly into Linux, and programs are pretty quick to startup despite the 900Mhz processor that powers the machine.
It has all of the standard ports you'd expect, 3 USB connectors, wired Ethernet (wireless is also built in), as well as a secure digital card slot for additional storage. The device also works great with the Verizon Wireless USB720 EV-DO modem for on-the-go access.
So while not exactly a powerhouse PC, it is a good machine to carry around and be able to get online, access the web, email, and remote into other computers via VNC or Remote Desktop. It also makes a great portable videoconference device via Skype. It is very easy to customize, and anyone with a little Linux knowledge can have some fun with this very handy device.