Is there a DesignMode property in WPF?

Indeed there is:

System.ComponentModel.DesignerProperties.GetIsInDesignMode

Example:

using System.ComponentModel;
using System.Windows;
using System.Windows.Controls;

public class MyUserControl : UserControl
{
    public MyUserControl()
    {
        if (DesignerProperties.GetIsInDesignMode(this))
        {
            // Design-mode specific functionality
        }
    }
}

In some cases I need to know, whether a call to my non-UI class is initiated by the designer (like if I create a DataContext class from XAML). Then the approach from this MSDN article is helpful:

// Check for design mode. 
if ((bool)(DesignerProperties.IsInDesignModeProperty.GetMetadata(typeof(DependencyObject)).DefaultValue)) 
{
    //in Design mode
}

Late answer, I know - but for anyone else who wants to use this in a DataTrigger, or anywhere in XAML in general:

xmlns:componentModel="clr-namespace:System.ComponentModel;assembly=PresentationFramework"

<Style.Triggers>
    <DataTrigger Binding="{Binding RelativeSource={RelativeSource Self}, 
                 Path=(componentModel:DesignerProperties.IsInDesignMode)}" 
                 Value="True">
        <Setter Property="Visibility" Value="Visible"/>
    </DataTrigger>
</Style.Triggers>