You have to provide a definition in a translation unit too, in case you use the value variable. That means, if for example you read its value.
The important thing is that the compiler is not required to give a warning or error if you violate that rule. The Standard says "no diagnostic required" for a violation.
In the next C++ Standard version, the rule changed. A variable is not used when it is used as a constant expression. Simply reading value above where the variable is initialized directly in the class means that still no definition is required then.
See the definition of use
in section 3.2 One Definition Rule
of the Standard and requirement for a definition for static data-members in 9.4.2, paragraph 4 and 5
(in the C++98 Standard. Appears in paragraph 3 and 4 in the n2800 draft of the next Standard).
Correction: The rule already changed for c++03: If the variable appears where a integral constant expression is required, no definition is needed (quoting from an unofficial revisions list for the 2003 update), see resolution for this language defect report:
An expression is potentially evaluated unless it appears where an integral constant expression is required (see 5.19), is the operand of the sizeof operator (5.3.3), or is the operand of the typeid operator and the expression does not designate an lvalue of polymorphic class type (5.2.8)...
Note that even then, many uses are in cases where an integral constant is not required. Cases where one is, is in array dimensions or in template metaprogramming. So strictly speaking (see this report), only the c++1x solution provides really guarantee that in obvious cases also like "s == string::npos"
where an integral constant is not required the definition of the static member is not needed, because the next Standard has a different, better wording of 3.2. This is however quite theoretical stuff, since most (all?) compiler don't moan anyway. Thanks for the guy in the comment section for telling me.