VIA is a company that has over the last several years carved out a niche innovating and making smaller and less power hungry processors and motherboards. These can be used to build computers that use as little as a standard incandescent light bulb including the monitor. That is a huge deal for someone using on-site power generation. These computers can be tiny and fanless, so the make almost no noise. VIA makes a few other initiatives including selling "carbon neutral" processors that they guarantee to plant a number of trees equal to the expected carbon output a the coal plant creates to power your computer.
Another type of computing that is even lower power has begun to take off, UMPCs and internet tablets are hand-held computers that can do all of the things I mentioned in the top of this post, except play DVDs, because they have no space for a disc drive. Nokia, the cellphone company, really opened up this category a couple of years ago, by making a sub $400 internet tablet. Many other companies now realize that price is very important for these devices. Sadly, Apple's iPhone and iPod Touch are not quite able to do all of these things, including browsing the internet like on a computer (they lack Flash support) and they lack support for an external keyboard.
The Asus Eee PC
The Asus Eee PC
If either of these options seems a little nerdy for you, remember that laptops generally use less power than desktops, and most people who think that the above options are too nerdy you probably don't need more expandability than laptops provide either, so you should go that route when getting your next computer. If you want a very limited but very small and inexpensive laptop, many people like the Asus Eee PC: It runs linux, has a tiny hard drive, and no optical (DVD) drive.