WPF Trigger based on Object Type

This is based on @AndyG's answer but is a bit safer because it's strongly typed.

Implement an IValueConverter named DataTypeConverter, which accepts an object and returns its Type (as a System.Type):

public class DataTypeConverter:IValueConverter
{
    public object Convert(object value, Type targetType, object parameter, 
      CultureInfo culture)
    {
        return value?.GetType() ?? Binding.DoNothing;
    }

    public object ConvertBack(object value, Type targetType, object parameter,
      CultureInfo culture)
    {
       throw new NotImplementedException();
    }
}

Change your DataTrigger to use the Converter, and set the value to the Type:

<DataTrigger Binding="{Binding SelectedItem,  
      Converter={StaticResource DataTypeConverter}}" 
      Value="{x:Type local:MyType}">
...
</DataTrigger>

Declare DataTypeConverter in the resources:

<UserControl.Resources>
    <v:DataTypeConverter x:Key="DataTypeConverter"></v:DataTypeConverter>
</UserControl.Resources>

If you are in a position to modify the (base) type assigned to 'SelectedItem' by adding the property:

public Type Type => this.GetType();

Then you could use the DataTrigger in xaml like this:

<DataTrigger Binding="{Binding SelectedItem.Type}" Value="{x:Type local:MyClass}">
</DataTrigger>

Advantage compared to AndyG's good answer is, that you do not have a magic string of your type in XAML, but have everything compile safe. Disadvantage: You need to modify your model - which might not always be possible.