Emacs has support for spell checking on demand (ispell) and as
your type (flyspell). Both packages depend on a copy of
ispell 3.2 or a compatible spell-checking program.
GNU Aspell is a popular choice these days, outdated Windows installers
are available from the official site.
Another possibility is Hunspell, which is available from
the ezwinports site. If you’re using the MSYS2 distribution, you can
install a recent version of either GNU Aspell or Hunspell through the
package manager Pacman. See Other useful ports.
Once installed, you will need to configure ispell-program-name
to tell ispell and flyspell to use aspell or
hunspell as a replacement for ispell. You can include the
full path to the aspell/hunspell binary, which means you
do not need to add its installation directory to the PATH.