I am compiling DCMTK on Microsoft Visual C++ (MSVC) and compilation fails with fatal error C1083: Cannot open include file: 'zlib.h': No such file or directory
You have not read the installation instructions in the INSTALL file! 
DCMTK needs some additional libraries such as zlib, libtiff etc. These can be downloaded in pre-compiled form from the DCMTK download page, see "Support libraries for Windows".