Fonts can be grouped in four main categories: basic, scripted, stylized and shapes.  The basic category is used most often for large amounts of text, and particularly for websites since browser cross-compatibility is a high priority in web design.  This group contain familiar fonts such as Arial, Times New Roman and Courier New,  the most web-friendly choices.  Also commonly used are Georgia, Verdana and Helvetica, and any of them will display a large amount of text nicely and offer a design a classic, sophisticated look.

Scripted fonts are better used as titles or in designs for dramatic effect.  These are elegant hand-written or brushed-look fonts.  Calligraphy is a common choice in this category as well and can bring class to a dull page of text and sometimes give an antiqued or scholarly look to a design.  Some of the more common scripted fonts are Bradley Hand, Brush Script, Edwardian, and Scriptina.

Similar to this group is the sylized category.  The less elegant hand-written fonts, such as Comic Sans, would belong here more than with the scripts.  They are useful for branding and theme design, Comic Sans used commonly for children's websites and print work.  Other stylized font examples would be LCD display , graffiti, characters made out of bones or other shapes, letters on fire or covered with snow.  Although not a good choice for large amounts of text, these fonts are great in a design or for large display text, and can really vitalize a website or printed page.

And lastly we have shapes.  Dingbats, webdings, animals, aliens, skeletons, snowflakes, shopping carts -- they all belong in this category.  Although totally worthless for text, these fonts are hugely useful for making icons, buttons, backgrounds, patterns, images, watermarks, and an endless list of other graphics.  Because fonts are vector images they can be used in any size without compromising quality, and can also be squeezed or stretched to any proportion.