Do I need an extern "C" block to include standard POSIX C headers?

The system C headers usually already include a extern "C" block, guarded by #ifdef __cplusplus. This way the functions automatically get declared as extern "C" when compiled as C++ and you don't need to do that manually.

For example on my system unistd.h and fcntl.h start with __BEGIN_DECLS and end with __END_DECLS, which are macros defined in sys/cdefs.h:

/* C++ needs to know that types and declarations are C, not C++.  */
#ifdef   __cplusplus
# define __BEGIN_DECLS  extern "C" {                                            
# define __END_DECLS }
#else
# define __BEGIN_DECLS
# define __END_DECLS
#endif

The behavior of <fcntl.h> and <unistd.h> in C++ is not specified by the standard (because they are also not part of the C89 standard). That said, I have never seen a platform where they (a) exist and (b) actually need to be wrapped in an extern "C" block.

The behavior of <stdio.h>, <math.h>, and the other standard C headers is specified by section D.5 of the C++03 standard. They do not require an extern "C" wrapper block, and they dump their symbols into the global namespace. However, everything in Annex D is "deprecated".

The canonical C++ form of those headers is <cstdio>, <cmath>, etc., and they are specified by section 17.4.1.2 (3) of the C++ standard, which says:

<cassert> <ciso646> <csetjmp> <cstdio> <ctime> <cctype> <climits>
<csignal> <cstdlib> <cwchar> <cerrno> <clocale> <cstdarg> <cstring>
<cwctype>

Except as noted in clauses 18 through 27, the contents of each header cname shall be the same as that of the corresponding header name.h, as specified in ISO/IEC 9899:1990 Programming Languages C (Clause 7), or ISO/IEC:1990 Programming Languages—C AMENDMENT 1: C Integrity, (Clause 7), as appropriate, as if by inclusion. In the C++ Standard Library, however, the declarations and definitions (except for names which are defined as macros in C) are within namespace scope (3.3.5) of the namespace std.

So the standard, non-deprecated, canonical way to use (e.g.) printf in C++ is to #include <cstdio> and then invoke std::printf.