Tomas Jogin wrote a bit about anti-aliasing and ClearType in Windows. I thought I’d chip in with my €.02.
The first thing I noted when I first laid eyes on OS X was the nice fonts. If you have a graphic card capable of OpenGL, OS X uses its Quartz Extreme engine to render the fonts and windows, which automatically provides a very nice anti-aliasing of fonts.
Windows 2000 and later also has anti-aliasing, but it’s not as good as the one in OS X. The main problem is that Windows doesn’t anti-alias fonts below a certain size, whereas OS X anti-aliases pretty much everything. (I have a vague memory of a registry setting where you can fiddle with this size threshold. I’ll look into it and report if I find anything.)
Windows 2000 and later Windows XP has a function called ClearType, which provides a sort of anti-aliasing. It is, however, not enabled out of the box, and for a good reason.
ClearType isn’t really supposed to be used on CRT monitors — it uses a technology called sub-pixel font rendering, which only provides an advantage if you have an LCD or TFT monitor.
On a CRT, a pixel is a point of light where three beams converge. These beams are red, green and blue and vary in strength to give the pixel a certain color.
An LCD monitor, however, has no cathode ray tube that shoots beams. Instead, each pixel on the screen is made of three individual diodes: red, green and blue. This means that an LCD screen with a resolution of 1024×768 really has a resolution of 3072×768.
Sub-pixel font rendering works by lighting individual pixel elements on an LCD screen, making the font smoother by effectively tripling the horisontal resolution.
On an LCD screen this looks nice and smooth. On a CRT screen, the results vary wildly — I find it less than good-looking, for reasons displayed in these pictures.

The top text uses “Standard” Windows anti-aliasing — meaning “none,” since the font size is too small to anti-alias, according to Windows. The bottom one uses ClearType. Now, let’s have a look up close and personal.

Here you see what sub-pixel font rendering looks like on a CRT screen: even though the text is black, you get various red, green and blue-tinted pixels. A CRT has no sub-pixel elements, so it gives the entire pixel an average color. The pixels on the left side of the letters are slightly red, whereas the ones to the right are slighly blue — this is the order in which LCD screens have their sub-pixel elements arranged: red-green-blue.
Below is the same image, but in gray-scale, approximating how it would look like if Windows used proper anti-aliasing:

If you take a few steps back and compare the images, you will probably find that the bottom one looks best on a CRT.
Update: I should also note that on an LCD screen, you can’t see these color artifacts at all. But on a CRT, I find that ClearType makes the text look blurred and hazy and a bit hard to focus on, due to the color artifacts.
Further reading