In the most common cases you can use the extracted icon bitmap data via the Icon.ToBitmap() method. You can save this image to different formats. However it is pretty hard to save the icon as "true" .ico file.
The problem is that there are no embedded encoders for icon images in .Net. So by default the result have been saved as low-color image. If this is unacceptable, the MS is recommended to save raw bitmap data as .ico manually. I suggest you use the IconLib library that already implement this task:
Icon icon = Icon.ExtractAssociatedIcon(@"C:WindowsSystem32
otepad.exe");
MultiIcon mIcon = new MultiIcon();
SingleIcon sIcon = mIcon.Add("notepad");
sIcon.CreateFrom(icon.ToBitmap(), IconOutputFormat.Vista);
sIcon.Save(@"c:
otepad.ico");