Solution 1:

You can achieve this with a DockPanel:

<DockPanel Width="300">
    <TextBlock>Left</TextBlock>
    <Button HorizontalAlignment="Right">Right</Button>
</DockPanel>

The difference is that a StackPanel will arrange child elements into single line (either vertical or horizontally) whereas a DockPanel defines an area where you can arrange child elements either horizontally or vertically, relative to each other (the Dock property changes the position of an element relative to other elements within the same container. Alignment properties, such as HorizontalAlignment, change the position of an element relative to its parent element).

Update

As pointed out in the comments you can also use the FlowDirection property of a StackPanel. See @D_Bester's answer.

Solution 2:

Yo can set FlowDirection of Stack panel to RightToLeft, and then all items will be aligned to the right side.

Solution 3:

For those who stumble upon this question, here's how to achieve this layout with a Grid:

<Grid>
    <TextBlock Text="Server:"/>
    <TextBlock Text="http://127.0.0.1" HorizontalAlignment="Right"/>
</Grid>

creates

Server:                                                                   http://127.0.0.1

Solution 4:

Could not get this working using a DockPanel quite the way I wanted and reversing the flow direction of a StackPanel is troublesome. Using a grid is not an option as items inside of it may be hidden at runtime and thus I do not know the total number of columns at design time. The best and simplest solution I could come up with is:

<Grid>
    <Grid.ColumnDefinitions>
        <ColumnDefinition Width="*" />
        <ColumnDefinition Width="Auto" />
    </Grid.ColumnDefinitions>
    <StackPanel Grid.Column="1" Orientation="Horizontal">
        <!-- Right aligned controls go here -->
    </StackPanel>
</Grid>

This will result in controls inside of the StackPanel being aligned to the right side of the available space regardless of the number of controls - both at design and runtime. Yay! :)

Solution 5:

This works perfectly for me. Just put the button first since you're starting on the right. If FlowDirection becomes a problem just add a StackPanel around it and specify FlowDirection="LeftToRight" for that portion. Or simply specify FlowDirection="LeftToRight" for the relevant control.

<StackPanel Orientation="Horizontal" HorizontalAlignment="Right" FlowDirection="RightToLeft">
    <Button Width="40" HorizontalAlignment="Right" Margin="3">Right</Button>
    <TextBlock Margin="5">Left</TextBlock>
    <StackPanel FlowDirection="LeftToRight">
        <my:DatePicker Height="24" Name="DatePicker1" Width="113" xmlns:my="http://schemas.microsoft.com/wpf/2008/toolkit" />    
    </StackPanel>
    <my:DatePicker FlowDirection="LeftToRight" Height="24" Name="DatePicker1" Width="113" xmlns:my="http://schemas.microsoft.com/wpf/2008/toolkit" />    
</StackPanel>