I'll have to agree with the masses. Times New Roman is probably the most over-used font on computers. It makes sense to use it when writing a paper, or something else you would print out and read. It just looks horrible when on websites though.
Most people don't know about the different types of fonts, and how they are used.
1. Serif: These fonts are used for documents that would be printed out and read. Serifs are those little bits on the edges of the letters that add "style" to the font. To see it, look at a document with Times New Roman at a very large font size. See the little accents on the ends of the 's' or bottom of the 'f'? That's a serif.
2. Sans-Serif: These fonts are used for viewing on a screen; computer monitor, TV... you get it. The word "sans" means "without." So Sans-Serif means "without serifs." If you look at a font like Verdana or Tahoma, they don't have the accents on the 's' or 'f'.
3. Monospace: Monospaced fonts are either Serif or Sans-Serif. The only difference is that each character takes up the same amount of space. This gives the impression that the fonts can be lined up vertically. These fonts are used in both print and screen mediums are are generally used when displaying code or computer output.
4. Cursive: These fonts usually look like handwriting, and are highly stylized. These aren't good for creating documents in because they can be hard to read, but Cursive fonts are good for purposely stylized text and logos.
5. Fantasy: This category is sort-of a "catch-all." Any fonts that don't fit in the above categories would fall under Fantasy. These can include scripted fonts depicting runes or glyphs, and can also be simply collections of characters like in Webdings and Wingdings.
So there you have it. The 5 default font types. I think everyone should try to learn more about what each type is used for and why. Especially web developers. Times New Roman is a very bad font to use when designing websites because it wasn't meant to be read on a screen. And I don't know about you, but I don't print out websites to read them.