Question

What are the exception classes that are included in the standard C++ library, and what should they be used for? I know there are a few new C++11 exceptions, but I’m not sure what they are or where they are.

Answer 1

std::exception <exception> interface (debatable if you should catch this)
    std::bad_alloc <new> failure to allocate storage
        std::bad_array_new_length <new> invalid array length
    std::bad_cast <typeinfo> execution of an invalid dynamic-cast
    std::bad_exception <exception> signifies an incorrect exception was thrown
    std::bad_function_call <functional> thrown by "null" std::function
    std::bad_typeid <typeinfo> using typeinfo on a null pointer
    std::bad_weak_ptr <memory> constructing a shared_ptr from a bad weak_ptr
    std::logic_error <stdexcept> errors detectable before the program executes
        std::domain_error <stdexcept> parameter outside the valid range
        std::future_error <future> violated a std::promise/std::future condition
        std::invalid_argument <stdexcept> invalid argument
        std::length_error <stdexcept> length exceeds its maximum allowable size
        std::out_of_range <stdexcept> argument value not in its expected range
    std::runtime_error <stdexcept> errors detectable when the program executes
        std::overflow_error <stdexcept> arithmetic overflow error.
        std::underflow_error <stdexcept> arithmetic underflow error.
        std::range_error <stdexcept> range errors in internal computations
        std::regex_error <regex> errors from the regular expression library.
        std::system_error <system_error> from operating system or other C API
            std::ios_base::failure <ios> Input or output error

Source: http://en.cppreference.com/w/cpp/error/exception
In practice, most exceptions are custom exceptions derived from logic_error and runtime_error. Not that these are neglected, but that many exceptions are domain specific.

Keep in mind that an exception should reflect what went wrong and not who threw it. (No "MyProgramException"s)