A little over a year ago, my family bought an eMac as our primary computer. It's seen a lot of use, more than any other computer I think I've ever owned. While it's a tad noisy (the fan isn't too quiet, and it's right there behind the screen in front of your face), and the old-school CRT runs warm (something particularly noticeable on hot summer days), it remains a very capable machine.
The latest eMac update changes very little—in comparison to ours, the newest models have only a slightly faster processor and a more skookum DVD recorder. While the newer Mac mini is much smaller and sexier, and can be set up to be a bit cheaper with a screen, the eMac is still more powerful and includes everything you need (keyboard, mouse, display), so it's worth looking at.