There is both a version of Emacs for X11, and for the terminal (emacs-nox). They both run on top of the Cygwin library. For the X11 version, you need an X server running.
Installation of the Emacs packages installs X11R6 and it takes ca. 100 MB. The Cygwin xserver (XWin.exe) runs fine. All works out of the box for english keyboards. For German keyboards you need an xmodmap file (see XModMap).
You can get xmodmap files for German keyboards here:
Startup for emacs -q --no-site-file:
NT Emacs: 0 seconds X11 Emacs: 9 seconds
Startup for Emacs with init files:
NT Emacs: 22 seconds X11 Emacs: 32 seconds
This includes tons of init files without any problem. Some things needs to be adjusted with the system-type ‘cygwin’ and ‘windows-nt’ especially for shell handling. So in general it looks like the elisp processing is as fast as with NT Emacs. In one personal package for example the Cygwin Emacs is faster than NT Emacs: Reading a 20000 line file and building a hash table with all the line offsets: Cygwin Emacs takes 3 seconds, NT Emacs takes 4 seconds.
One thing that I dislike is the old Athena widget set scrollbar but this should really not be a problem.
So my conclusion is that it’s stable and works perfect.
Just to make sure, this information applies to the X11 Emacs. I just downloaded the current (March 2010, v.23.1.10), terminal version (emacs-nox.exe) using Cygwin setup to give it a quick try, and found that it runs in the same window as it is started from, has no mouse support, and a quick inspection indicates that it has lots of deficiencies. See also NTEmacsWithCygwin and CygwinizedEmacsHOWTO. – KristjánJónasson