NB : this has changed since C++11, read other answers too
You need to define static variables in a translation unit, unless they are of integral types.
In your header:
private:
static const char *SOMETHING;
static const int MyInt = 8; // would be ok
In the .cpp file:
const char *YourClass::SOMETHING = "something";
C++ standard, 9.4.2/4:
If a static data member is of const
integral or const enumeration type,
its declaration in the class
definition can specify a
constant-initializer which shall be an
integral constant expression. In that
case, the member can appear in
integral constant expressions within
its scope. The member shall still be
defined in a namespace scope if it is
used in the program and the namespace
scope definition shall not contain an
initializer.