How do I create a WPF Rounded Corner container?

You don't need a custom control, just put your container in a border element:

<Border BorderBrush="#FF000000" BorderThickness="1" CornerRadius="8">
   <Grid/>
</Border>

You can replace the <Grid/> with any of the layout containers...

I know that this isn't an answer to the initial question ... but you often want to clip the inner content of that rounded corner border you just created.

Chris Cavanagh has come up with an excellent way to do just this.

I have tried a couple different approaches to this ... and I think this one rocks.

Here is the xaml below:

<Page
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Background="Black"
>
    <!-- Rounded yellow border -->
    <Border
        HorizontalAlignment="Center"
        VerticalAlignment="Center"
        BorderBrush="Yellow"
        BorderThickness="3"
        CornerRadius="10"
        Padding="2"
    >
        <Grid>
            <!-- Rounded mask (stretches to fill Grid) -->
            <Border
                Name="mask"
                Background="White"
                CornerRadius="7"
            />

            <!-- Main content container -->
            <StackPanel>
                <!-- Use a VisualBrush of 'mask' as the opacity mask -->
                <StackPanel.OpacityMask>
                    <VisualBrush Visual="{Binding ElementName=mask}"/>
                </StackPanel.OpacityMask>

                <!-- Any content -->
                <Image Source="http://chriscavanagh.files.wordpress.com/2006/12/chriss-blog-banner.jpg"/>
                <Rectangle
                    Height="50"
                    Fill="Red"/>
                <Rectangle
                    Height="50"
                    Fill="White"/>
                <Rectangle
                    Height="50"
                    Fill="Blue"/>
            </StackPanel>
        </Grid>
    </Border>
</Page>

I just had to do this myself, so I thought I would post another answer here.

Here is another way to create a rounded corner border and clip its inner content. This is the straightforward way by using the Clip property. It's nice if you want to avoid a VisualBrush.

The xaml:

<Border
    Width="200"
    Height="25"
    CornerRadius="11"
    Background="#FF919194"
>
    <Border.Clip>
        <RectangleGeometry
            RadiusX="{Binding CornerRadius.TopLeft, RelativeSource={RelativeSource AncestorType={x:Type Border}}}"
            RadiusY="{Binding RadiusX, RelativeSource={RelativeSource Self}}"
        >
            <RectangleGeometry.Rect>
                <MultiBinding
                    Converter="{StaticResource widthAndHeightToRectConverter}"
                >
                    <Binding
                        Path="ActualWidth"
                        RelativeSource="{RelativeSource AncestorType={x:Type Border}}"
                    />
                    <Binding
                        Path="ActualHeight"
                        RelativeSource="{RelativeSource AncestorType={x:Type Border}}"
                    />
                </MultiBinding>
            </RectangleGeometry.Rect>
        </RectangleGeometry>
    </Border.Clip>

    <Rectangle
        Width="100"
        Height="100"
        Fill="Blue"
        HorizontalAlignment="Left"
        VerticalAlignment="Center"
    />
</Border>

The code for the converter:

public class WidthAndHeightToRectConverter : IMultiValueConverter
{
    public object Convert(object[] values, Type targetType, object parameter, CultureInfo culture)
    {
        double width = (double)values[0];
        double height = (double)values[1];
        return new Rect(0, 0, width, height);
    }
    public object[] ConvertBack(object value, Type[] targetTypes, object parameter, System.Globalization.CultureInfo culture)
    {
        throw new NotImplementedException();
    }
}