If you have a mime type and you want to find the default extension for it, you can get this from the Extension value in the following registry key:

HKEY_CLASSES_ROOT\MIME\Database\Content Type\<mime type>

    public static string GetDefaultExtension(string mimeType)
    {
      string result;
      RegistryKey key;
      object value;

      key = Registry.ClassesRoot.OpenSubKey(@"MIME\Database\Content Type\" + mimeType, false);
      value = key != null ? key.GetValue("Extension", null) : null;
      result = value != null ? value.ToString() : string.Empty;

      return result;
    }

One the other hand, if you have a file extension and you want to know what that mime type is, you can get that via the Content Type value of this key:

HKEY_CLASSES ROOT\<extension>

    public static string GetMimeTypeFromExtension(string extension)
    {
      string result;
      RegistryKey key;
      object value;

      if (!extension.StartsWith("."))
        extension = "." + extension;

      key = Registry.ClassesRoot.OpenSubKey(extension, false);
      value = key != null ? key.GetValue("Content Type", null) : null;
      result = value != null ? value.ToString() : string.Empty;

      return result;
    }