See intro blogpost here.
  UPDATE Feb. 29, 2012: As hinted at below that this would happen, this blogpost on dependency properties is now outdated. Since the Consumer Preview of Windows 8 released, dependency properties now work exactly like they do in Silverlight and WPF. 
  ---
  Declaration of dependency properties has changed in the WinRT. This is a temporary change and will go away when WinRT hits beta, but still good to know if you start prototyping on WinRT today. If you are a control developer this is probably one of the things you would have to change in the most places.
  Here’s what the API looks like for Silverlight and WPF for registering a Dependency Property or an Attached Property:
  public static DependencyProperty Register(
      string name, 
      Type propertyType, 
      Type ownerType,
      PropertyMetadata typeMetadata);
public static DependencyProperty RegisterAttached(
      string name, 
      Type propertyType,
      Type ownerType, 
      PropertyMetadata defaultMetadata);
And here’s what this currently looks like in WinRT CTP :
public static DependencyProperty Register(
      string name, 
      string propertyTypeName, 
      string ownerTypeName,
      PropertyMetadata typeMetadata);
public static DependencyProperty RegisterAttached(
      string name, 
      string propertyTypeName,
      string ownerTypeName, 
      PropertyMetadata defaultMetadata);
Notice how the PropertyType and PropertyOwnerType is now strings instead of types!
This means you would have to write your code like this to make it cross-compile:
        public double MyDoubleProperty
        {
            get { return (double)GetValue(MyDoublePropertyProperty); }
            set { SetValue(MyDoublePropertyProperty, value); }
        }
        public static readonly DependencyProperty MyDoublePropertyProperty =
            DependencyProperty.Register("MyDoubleProperty", 
#if NETFX_CORE
             "Double", "MyNamespace.MyControl", 
#else
                typeof(double), typeof(MyNamespace.MyControl), 
#endif
                 new PropertyMetadata(0d));
Also note that you don’t use the full type name for the system types. Ie. here you use “Double” and not “double” or “System.Double”.
You could create a few static methods to replace the Register/RegisterAttached methods that will make your code cross-platform, and switch it out just there when this changes. Here’s one example how this could be accomplished (the ‘ToRTString’ method isn’t fully tested though…):
    public static DependencyProperty RegisterAttached(string name, Type propertyType, Type ownerType, PropertyMetadata metadata)
    {
        return DependencyProperty.RegisterAttached(name, 
#if NETFX_CORE
            propertyType.ToRTString(), ownerType.ToRTString()
#else
            propertyType, ownerType
#endif
            , metadata);
    }
    public static DependencyProperty Register(string name, Type propertyType, Type ownerType, PropertyMetadata metadata)
    {
        return DependencyProperty.Register(name,
#if NETFX_CORE
            propertyType.ToRTString(), ownerType.ToRTString()
#else
            propertyType, ownerType
#endif
            , metadata);
    }
#if NETFX_CORE
    private static string ToRTString(this Type type)
    {
        string name = type.FullName;
        if(name.StartsWith("System."))
            return name.Substring(7);
        else
            return name;
    }
#endif