Richard rutter, nathan ford and amrinder sandhu, among others, have written extensively about extending the number of fonts available to web designers. The basic font stacks are based on a lowest common denominator approach, selecting only those fonts common to all computers. There are however, a significant number of fonts installed on a large percentage of computers which could be added to the basic stacks. This would allow those users with the fonts installed to view pages set in those fonts, while degrading to the basic stacks for those users who do not. In the example below, Garamond has been added to the front of the serif font stack. Users with Garamond installed will now have their page set in Garamond while those that don't will see Georgia.

{font-family:Garamond, Georgia, Times, serif;}

In this way it is possible to extend the basic font stacks significantly. As well as increasing the availability of typefaces this approach also facilitates other operating systems such as Linux which have a different set of fonts installed. The tables below give a good indication of current font availability.

Richard Rutter has devised a font matrix which is a useful tool in determining font availability across Windows and Mac operating systems. The matrix dates from 2007, so the tables below should be more accurate.

Think about typefaces beyond the core web fonts.
― Richard Rutter, skillswap '09

Most common fonts on Windows (Dec 2011)

Serif % Sans-serif %
Georgia 99.48 Verdana 99.84
Times New Roman 99.69 Tahoma 99.95
Palatino Linotype 99.42 Arial 99.84
Book Antiqua 86.09 Trebuchet MS 99.74
Garamond 86.24 Lucida Sans Unicode 99.37
Cambria 54.51 Franklin Gothic Medium 97.87
Constantia 53.81 Calibri 54.76
Goudy Old Style 51.30 Candara 54.31
Baskerville Old Face 49.10 Gill Sans MT 51.74
Bodoni MT 47.89 Segoe UI 45.04

Most common fonts on Mac (Dec 2011)

Serif % Sans-serif %
Times 99.37 Helvetica 100
Georgia 97.63 Geneva 98.84
Times New Roman 97.63 Lucida Grande 100
Hoefler Text 88.70 Arial 98.73
Baskerville 88.60 Verdana 99.05
Didot 87.72 Helvetica Neue 98.58
Big Caslon 85.10 Trebuchet MS 94.2
Palatino 79.71 Gill Sans 91.52
Lucida Bright 99.68 Futura 91.01
Garamond 23.84 Optima 90.14

Most common fonts on linux (Dec 2011)

Serif % Sans-serif %
Century Schoolbook 99.28 URW Gothic L 99.28
URW Bookman L 98.81 Nimbus Sans L 98.57
URW Palladio L 98.57 Deja Vu Sans 97.37
Nimbus Roman 98.33 Deja Vu Sans Light 94.94
Deja Vu Serif 97.37 Deja Vu Sans Condensed 91.17
Bitstream Charter 92.36 Free Sans 84.01

Source: Codestyle font survey

Nathan Ford has a detailed examination of improved font stacks grouped by serif / sans-serif / monospaced and by individual typeface characteristics, such as x-height and narrow face or condensed. He further breaks down the font stacks into suitability for paragraphs and titles.
The list below is a selection of his paragraph choices.

Serif

Baskerville, Times, “Times New Roman”, serif
Garamond, “Hoefler Text”, Palatino, “Palatino Linotype”, serif
Georgia, Palatino,” Palatino Linotype”, Times, “Times New Roman”, serif
Cambria, Georgia, Times, “Times New Roman”, serif
“Copperplate Light”, “Copperplate Gothic Light”, serif
Georgia, Times, “Times New Roman”, serif
Palatino, “Palatino Linotype”, Georgia, Times, “Times New Roman”, serif
Palatino, “Palatino Linotype”, “Hoefler Text”, Times, “Times New Roman”, serif
Times, “Times New Roman”, Georgia, serif

Sans-serif

Geneva, “Lucida Sans”, “Lucida Grande”, “Lucida Sans Unicode”, Verdana, sans-serif
Arial, “Helvetica Neue”, Helvetica, sans-serif
“Century Gothic”, “Apple Gothic”, sans-serif
“Franklin Gothic Medium”, “Arial Narrow Bold”, Arial, sans-serif
Futura, “Century Gothic”, AppleGothic, sans-serif
“Gill Sans”, Calibri, “Trebuchet MS”, sans-serif
“Helvetica Neue”, Arial, Helvetica, sans-serif
Impact, Haettenschweiler, “Arial Narrow Bold”, sans-serif
“Lucida Sans”, “Lucida Grande”, “Lucida Sans Unicode”, sans-serif
Tahoma, Geneva, Verdana, sans-serif
“Trebuchet MS”, “Lucida Sans Unicode”, “Lucida Grande”, Arial, sans-serif
“Trebuchet MS”, Tahoma, Arial, sans-serif - t Verdana, Geneva, Tahoma, sans-serif
Verdana, Tahoma, Geneva, sans-serif

Monospace

Consolas, “Lucida Console”, Monaco, monospace
“Courier New”, Courier, monospace

Printer fonts versus screen fonts

Many of the fonts listed above are digitised versions of printer fonts. While they will display reasonably well across the various systems, fonts designed for screen will be more legible. Typefaces designed specifically for screen are more open and serifs faces have less contrast between the thick and this strokes leading to improved legibility on-screen.

comparison of open and closed typeface designs

Cambria, Constantia and Georgia are common serif faces which have been designed specifically for use on-screen. Calibri, Verdana, Lucida (various), Tahoma and Trebuchet MS are the equivalent sans-serif faces. Consequently, this writer suggests the following font-stacks ―

Serif

Cambria, Georgia, Times, “Times New Roman”, serif

SAns-Serif

Calibri, "Lucida Grande", "Lucida Sans", Verdana, sans-serif

In Summary

Extended font stacks are a valuable addition to the core web fonts. With the font-stacks suggested, and according to the statistics above, 54.5% of Windows users will view a page using this font-stack page in Cambria, and all but 0.5% will view it in Georgia. Cambria is available on 40.82% of Macs and Georgia is available to 97.63%, leaving 2.3% defaulting to Times.
Extended font stacks can definitely improve the individual character of a website for a majority of users.