Removing Cygwin from your windows machine can become quite a task at times. Here is the 3 step process which I followed to uninstall Cygwin
On the Command prompt type following commands in order –
1) C:\>takeown /r /d y /f cygwin
Read this command properly; It is takeown & not takedown.
2) icacls cygwin /t /grant Everyone:F
3) rmdir /s /q cygwin