There is a wide range of symbols available for use with TeX, most of which are not shown (or even mentioned) in (La)TeX books. The Comprehensive LaTeX Symbol List (by Scott Pakin et al.) illustrates over 2000 symbols, and details the commands and the LaTeX packages needed to produce them.
However, while the symbol list is a wonderful resource, it is never easy to find a particular symbol there. A graphical symbol search is available on the web. The site provides you a scratch area on which you draw the symbol you’re thinking of, with your mouse; when you’ve finished drawing, the classifier tries to match your sketch with symbols it knows about. The matching process is pretty good, even for the sketches of a really poor draughtsman (such as the present author), and it’s often worth trying more than once. ‘Detexify apps’ are available for both Android and iPhone devices, you can use them to draw the symbol with your fingertip — a less challenging procedure than using your workstation’s mouse, by all accounts!
If you are using Unicode maths in XeTeX or LuaTeX, your own distribution ought to provide the Unicode maths symbol table unimath-symbols.pdf; this lists the things available in the commonly-used mathematics fonts. (If the file isn’t already available on your system, you can download it from CTAN, where it live with the unicode-math package.
Other questions in this FAQ offer specific help on kinds of symbols:
This answer last edited: 2012-09-03