GNU Aspell is a freeware / open source spelling checker. It is used by many text editors, web browsers etc. Aspell has been ported to many Unix-like operating systems as well as to Windows. (However, the Windows version is usually several versions behind the Unix versions.)
Dictionaries for many languages are available. However, Aspell works best with English language. Not all dictionaries have been compiled for Windows.
Aspell can be used as a stand-alone program, or it can be called from other programs by using so called pipe mode, or by calling the DLLs directly. Vedit implementation uses the pipe mode.
For more information, see the homepage of GNU Aspell.