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
Dependency properties are used when you want data binding in a `UserControl`, and is the standard method of data binding for the WPF Framework controls. DPs have [slightly better binding performance](https://stackoverflow.com/questions/570684/inotifypropertychanged-vs-dependencyproperty), and everything is provided to you when inside a `UserControl` to implement them.

Otherwise, you typically use `INotifyPropertyChanged` for binding elsewhere, since it's easier to implement in stand-alone classes and has less overhead. As far as your original assumptions:

1. There is a local instance of your variable, you definitely do not save any overhead over a property since there is significant data binding logic built-in.
2. [They must be accessed on the main thread](https://stackoverflow.com/a/783154/93306).