How do I set variables to, or test for IEEE NaN (``Not a Number'') and other special values?

Many systems with high-quality IEEE floating-point implementations provide facilities (e.g. predefined constants, and functions like isnan(), either as nonstandard extensions in <math.h> or perhaps in<ieee.h> or <nan.h>) to deal with these values cleanly, and work is being done to formally standardize such facilities. A crude but usually effective test for NaN can be written based on the fact that IEEE NaN's never compare equal to anything, even themselves; therefore a number that doesn't compare equal to itself must be a NaN:
#define isnan(x) ((x) != (x))

Beware, though, that non-IEEE-aware compilers may optimize the test away. (Note also that even if you do have a predefined constant like NAN, you cannot use it in comparisons like if(x == NAN), again because NaN's do not compare equal to themselves.)
C99 provides isnan(), fpclassify(), and several other classification routines.
Another possibility is to format the value in question using sprintf: on many systems it generates strings like "NaN" and "Inf" which you could compare for in a pinch.
To initialize variables with these values (and if your system does not provide cleaner solutions), you may be able to get away with some compile-time ``arithmetic'':
double nan = 0./0.;
double inf = 1./0.;

Don't be too surprised, though, if these don't work (or if they abort the compiler with a floating-point exception).
(The most reliable way of setting up these special values would use a hex representation of their internal bit patterns, but initializing a floating-point value with a bit pattern would require using a union or some other type punning mechanism and would obviously be machine-dependent.)