Question: When should I use dependency properties in WPF?

They are static, so we save a lot on memory, compared to using .NET properties.
Other gains of using dependency properties over .NET properties are:
1) no need to check thread access
2) prompt a containing element to be rendered
etc...

So it seems I should ALWAYS use dependency properties in my projects where I use WPF?

Maybe for some trivial properties of helper classes here and there I could
get away with .NET properties...

Answer: 
Dependency Property is a broad concept to explain which might take couple of pages to write. So just to answer your main question, Dependency property is used where

1. You know the property is going to be the binding target i.e you are creating a user control/custom control and want property that should be binding driven.
2. You want automatic property change notifications (coerse and validation also).
3. We want value inheritance in styles,themes, parent or default value.
4. There is not need to create the properties on Model or ViewModel layer as dependency properties most of the time as that is not going to help much on memory saving front as most of the properties we define in model/VM will have values per instance as they will be constantly changing. Resolving Dependency property value is a burden in itself so making property dependency unnecessarily is not advisable.

Thanks
Perhaps you should take another look at the [Dependency Properties Overview](http://msdn.microsoft.com/en-us/library/ms752914.aspx) page at MSDN. 

Personally, I would only ever create a `DependencyProperty` when I really *need* to. For the most part, I use normal CLR properties in data type and view model classes to bind to... this is absolutely fine, as long as I implement the `INotifyPropertyChanged` interface.

So for all of my usual data bindings, I use normal CLR properties. I *only* declare a `Dependency Property` in order to provide some added functionality in a `UserControl`.