It is a good idea to have commands such as \R for the real numbers and
other standard number sets. Traditionally these were typeset in bold.
Because mathematicians usually do not have access to bold chalk, they
invented the special symbols that are now often used for \R, \C,
etc. These symbols are known as "blackboard bold". Before
insisting on using them, consider whether going back to the old system
of ordinary bold might not be acceptable (it is certainly simpler).
A set of blackboard bold capitals is available in the AMS "msbm" fonts ("msbm" is available at a range of design sizes, with names such as "msbm10"). The pair of font families (the other is called "msam") have a large number of mathematical symbols to supplement the ones in the standard TeX distribution, and are available in Type 1 format with most modern distributions. Support files for using the fonts, both under Plain TeX and LaTeX (packages amssymb and amsfonts), are available.
Another complete set of blackboard bold fonts written in Metafont is the bbold family. This set has the interesting property of offering blackboard bold forms of lower-case letters, something rather rarely seen on actual blackboards; the font source directory also contains sources for a LaTeX package that enables use of the fonts. The fonts are not available in Type 1 format.
An alternative source of Type 1 fonts with blackboard bold characters may be found in the steadily increasing set of complete families, both commercial and free, that have been prepared for use with (La)TeX (see "choice of outline fonts"). Of the free sets, the txfonts and pxfonts families both come with replicas of msam and msbm, and the mathpazo family includes a "mathematically significant" choice of blackboard bold characters.
The "lazy person's" blackboard bold macros:
\newcommand{\R}{{\sf R\hspace*{-0.9ex}%
\rule{0.15ex}{1.5ex}\hspace*{0.9ex}}}
\newcommand{\N}{{\sf N\hspace*{-1.0ex}%
\rule{0.15ex}{1.3ex}\hspace*{1.0ex}}}
\newcommand{\Q}{{\sf Q\hspace*{-1.1ex}%
\rule{0.15ex}{1.5ex}\hspace*{1.1ex}}}
\newcommand{\C}{{\sf C\hspace*{-0.9ex}%
\rule{0.15ex}{1.3ex}\hspace*{0.9ex}}}
work well at normal size if the surrounding text is cmr10. However,
they are not part of a proper maths font, and so do not work in sub- and
superscripts. Moreover, the size and position of the vertical bar can be
affected by the font of the surrounding text.