These are the headers that my library implementation includes.
The Standard C++ library consists of 51 required headers. This implementation also includes three additional headers, <hash_map>, <hash_set>, and <slist>, not required by the C++ Standard, for a total of 54 headers. Of these 54 headers, 16 constitute the Standard Template Library, or STL. These are indicated below with the notation (STL):

<algorithm> -- (STL) for defining numerous templates that implement useful algorithms
<bitset> -- for defining a template class that administers sets of bits
<complex> -- for defining a template class that supports complex arithmetic
<deque> -- (STL) for defining a template class that implements a deque container
<exception> -- for defining several functions that control exception handling
<fstream> -- for defining several iostreams template classes that manipulate exteral files
<functional> -- (STL) for defining several templates that help construct predicates for the templates defined in <algorithm> and <numeric>
<map> -- (STL) for defining template classes that implement hashed associative containers that map keys to values
<hash_set> -- (STL) for defining template classes that implement hashed associative containers
<iomanip> -- for declaring several iostreams manipulators that take an argument
<ios> -- for defining the template class that serves as the base for many iostreams classes
<iosfwd> -- for declaring several iostreams template classes before they are necessarily defined
<iostream> -- for declaring the iostreams objects that manipulate the standard streams
<istream> -- for defining the template class that performs extractions
<iterator> -- (STL) for defining several templates that help define and manipulate iterators
<limits> -- for testing numeric type properties
<list> -- (STL) for defining a template class that implements a doubly linked list container
<locale> -- for defining several classes and templates that control locale-specific behavior, as in the iostreams classes
<map> -- (STL) for defining template classes that implement associative containers that map keys to values
<memory> -- (STL) for defining several templates that allocate and free storage for various container classes
<new> -- for declaring several functions that allocate and free storage
<numeric> -- (STL) for defining several templates that implement useful numeric functions
<ostream> -- for defining the template class that performs insertions
<queue> -- (STL) for defining a template class that implements a queue container
<set> -- (STL) for defining template classes that implement associative containers
<slist> -- (STL) for defining a template class that implements a singly linked list container
<sstream> -- for defining several iostreams template classes that manipulate string containers
<stack> -- (STL) for defining a template class that implements a stack container
<stdexcept> -- for defining several classes useful for reporting exceptions
<streambuf> -- for defining template classes that buffer iostreams operations
<string> -- for defining a template class that implements a string container
<strstream> -- for defining several iostreams classes that manipulate in-memory character sequences
<typeinfo> -- for defining class type_info, the result of the typeid operator
<utility> -- (STL) for defining several templates of general utility
<valarray> -- for defining several classes and template classes that support value-oriented arrays
<vector> -- (STL) for defining a template class that implements a vector container

The Standard C++ library works in conjunction with the 18 headers from the Standard C library, sometimes with small alterations. The headers come in two forms, new and traditional. The new-form headers are:

<cassert> -- for enforcing assertions when functions execute
<cctype> -- for classifying characters
<cerrno> -- for testing error codes reported by library functions
<cfloat> -- for testing floating-point type properties
<ciso646> -- for programming in ISO 646 variant character sets
<climits> -- for testing integer type properties
<clocale> -- for adapting to different cultural conventions
<cmath> -- for computing common mathematical functions
<csetjmp> -- for executing nonlocal goto statements
<csignal> -- for controlling various exceptional conditions
<cstdarg> -- for accessing a varying number of arguments
<cstddef> -- for defining several useful types and macros
<cstdio> -- for performing input and output
<cstdlib> -- for performing a variety of operations
<cstring> -- for manipulating several kinds of strings
<ctime> -- for converting between various time and date formats
<cwchar> -- for manipulating wide streams and several kinds of strings
<cwctype> -- for classifying wide characters
Note that it also includes the following deprecated standard C library headers and the old non-standard C++ library headers.
The traditional Standard C library headers are:

<assert.h> -- for enforcing assertions when functions execute
<ctype.h> -- for classifying characters
<errno.h> -- for testing error codes reported by library functions
<float.h> -- for testing floating-point type properties
<iso646.h> -- for programming in ISO 646 variant character sets
<limits.h> -- for testing integer type properties
<locale.h> -- for adapting to different cultural conventions
<math.h> -- for computing common mathematical functions
<setjmp.h> -- for executing nonlocal goto statements
<signal.h> -- for controlling various exceptional conditions
<stdarg.h> -- for accessing a varying number of arguments
<stddef.h> -- for defining several useful types and macros
<stdio.h> -- for performing input and output
<stdlib.h> -- for performing a variety of operations
<string.h> -- for manipulating several kinds of strings
<time.h> -- for converting between various time and date formats
<wchar.h> -- for manipulating wide streams and several kinds of strings
<wctype.h> -- for classifying wide characters

Finally, in this implementation, the Standard C++ library also includes several headers for compatibility with traditional C++ libraries:

<fstream.h> -- for defining several iostreams template classes that manipulate exteral files
<iomanip.h> -- for declaring several iostreams manipulators that take an argument
<iostream.h> -- for declaring the iostreams objects that manipulate the standard streams
<new.h> -- for declaring several functions that allocate and free storage
<stl.h> -- for declaring several template classes that aid migration from older versions of the Standard Template Library