Updates (2011-02-20): Cygwin patches did not make it into GT5.0.3, but they may make it into a future release.
Updates (2010-12-08): Binghamton University TeraGrid has written up instructions for applying the patches and getting GT compiled. Also, it appears new versions of GT will be coming out over the next few months. I plan to check them out for Cygwin compatibility.
If you are interested in compiling Globus Toolkit 5.0.2 on Cygwin, I have some simple patches that seem to get the job done. Perhaps they will make it into the next release. For now: http://lists.globus.org/pipermail/gt-dev/2010-September/001885.html
Note that I built this on Cygwin 1.7; Cygwin 1.5 will probably not work. Also you must have the gcc4.x Cygwin packages (C and C++) installed. Getting GT to build on gcc3.x is probably not much more work, but going with gcc4 is easier than worrying about unrecognized compiler flags all over the place.
You also need to specify the flag: --with-buildopts="-static=1" when running the main configure script. Building GT on Cygwin with dynamic linking is certainly beyond me, and is a pretty big undertaking, so this tells it to use only static linking. I recommend --with-buildopts="-verbose -static=1" so you can also see what is going on.
(For the record, on dynamic linking: I tried adding some flags to configure.ac or configure.in to let autoconf know that we wanted to make DLLs and do dynamic linking. But trying to run a modern version of autoreconf generated configure scripts that don't work with the GT package. Even if the build worked, this probably wouldn't be a good idea as making DLLs properly requires going through all the source and making sure data exports are handled correctly. At least one package (globus_libtool) is DLL ready and already generates a DLL and RTL properly, so we know it all works theoretically once the individual libraries are DLL ready. There may be other subpackages that are DLL ready, but they will probably have to be handled one at a time. Unfortunately, GPT doesn't really offer a method to build the whole Globus Toolkit with some parts statically linked and some dynamic.)
If you get a build failure with an error like "fork()" or "vfork()" "resource temporarily unavailable", this means your machine ran out of processes while building (due to what I'm going to call a "process leak" bug). Basically just rerun make and it should get farther each time before crashing, until finally it gets all the way through. Or build GT in smaller chunks; if you are just trying to get proxy certificate running you only really need "make gsi-myproxy gsi-openssh".
You may also have to circumvent GPT's somewhat outdated Perl libraries. If you have a problem getting Archive::Tar to open some of the source packages, then you should install the Cygwin CPAN package and then use that to install an updated version of Archive::Tar. You may then need to hide GPT's versions under $GLOBUS_LOCATION/sbin/perl.
Feel free to ping me with any questions/thoughts.