On a standards-conforming C++ implementation, no. The ordinary form of new will never return NULL; if allocation fails, a std::bad_alloc exception will be thrown (the new (nothrow) form does not throw exceptions, and will return NULL if allocation fails).
On some older C++ compilers (especially those that were released before the language was standardized) or in situations where exceptions are explicitly disabled (for example, perhaps some compilers for embedded systems), new may return NULL on failure. Compilers that do this do not conform to the C++ standard.