Here are all fonts available (with samples and source code) in TeX Live in Ubuntu:
http://www.tug.dk/FontCatalogue/
It isn't the latest complete font list of TeX Live/MacTeX 2010, but still very useful.
Another good source for free fonts in LaTeX, is
http://www.ctan.org/tex-archive/info/Free_Math_Font_Survey/survey.html
For a complete list of fonts in your computer, you have to check the installation path of TeX Live, say, somepath/texmf-dist/fonts/. But it is difficult to know how to use the fonts, since some fonts are not well-documented. You can also see this older question:
What fonts are installed on my box?
You don't have to use XeTeX to access these fonts. On the other hand, XeTeX helps you to use font installed in your OS easily, like 'Times New Roman' in MacOS and Windows.
Usually, you may want to use a uniqe font theme in one document. There're many font package for this purpose. Use the packages to change the serif, sans serif and monosapce typefaces, and also the math font if there is. You can know many packages from the two big-lists I mentioned.
For example,
\documentclass{article}
\usepackage{fourier}
You'll get Utopia text font and Fourier math font in your document. Other common font packages include txfonts, pxfonts, mathdesign etc.
If you just want to use a special font for a few text, you will probably not want to change the typeface of whole document. Some font packages (especially fonts for symbols and non-latin alphabets) provide some commands for this. These packages are often well documented. An example:
% \usepackage{tipa} % font package for International Phonetic Alphabet
Pronounce \textipa{["lA:tEk]} or \textipa{["leItEk]}
However, there are many fonts without a .sty package with a PDF document, even no sample code and result. You have to use LaTeX's font commands to access the font by name. (See the big-lists to know the font names.)
In NFSS scheme, you may use, for example:
{\fontfamily{cmfib}\selectfont Computer Modern Fibonacci} % ref cmfonts.fdd
Another example:
{\usefont{OT1}{pbk}{db}{sc} Adobe Bookman Demibold Smallcaps} % ref psnfss
You may want to know more about LaTeX2e NFSS scheme. See fntguide or any book on LaTeX.