How to set WPF window's startup ClientSize?

You can do it in code-behind on the Load event handler in one of two ways:

NOTE: The content of the LayoutRoot Grid is the same in both examples, but the Width and Height on the LayoutRoot are only specified in example A.

A) ClearValue on the the Window's SizeToContent and on the content's Width and Height:

using System.Windows;

namespace WpfWindowBorderTest
{
    /// <summary>
    /// Interaction logic for Window1.xaml
    /// </summary>
    public partial class Window1 : Window
    {
        public Window1()
        {
            InitializeComponent();
        }

        private void Window_Loaded(object sender, RoutedEventArgs e)
        {
            ClearValue(SizeToContentProperty);
            LayoutRoot.ClearValue(WidthProperty);
            LayoutRoot.ClearValue(HeightProperty);
        }
    }
}

assuming a page layout like (note the SizeToContent setting and Loaded event handler on the Window and the Width and Height specified on the LayoutRoot):

<Window x:Class="WpfWindowBorderTest.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1" SizeToContent="WidthAndHeight" Loaded="Window_Loaded">
    <Grid x:Name="LayoutRoot" Width="300" Height="300" Background="Green">
        <Grid.RowDefinitions>
            <RowDefinition Height="1*"/>
            <RowDefinition Height="3*"/>
        </Grid.RowDefinitions>
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="1*"/>
            <ColumnDefinition Width="3*"/>
        </Grid.ColumnDefinitions>
        <Rectangle Grid.Row="0" Grid.Column="0" Fill="Black" />
        <Rectangle Grid.Row="0" Grid.Column="0" Width="75" Height="75" Fill="Red" />
        <Rectangle Grid.Row="1" Grid.Column="1" Fill="Yellow" />
        <Rectangle Grid.Row="1" Grid.Column="1" Width="225" Height="225" Fill="Red" />
    </Grid>
</Window>

or

B) setting the Window's Width and Height accounting for the System-specific client window frame sizes:

using System.Windows;

namespace WpfWindowBorderTest
{
    /// <summary>
    /// Interaction logic for Window1.xaml
    /// </summary>
    public partial class Window1 : Window
    {
        public Window1()
        {
            InitializeComponent();

            const int snugContentWidth = 300;
            const int snugContentHeight = 300;

            var horizontalBorderHeight = SystemParameters.ResizeFrameHorizontalBorderHeight;
            var verticalBorderWidth = SystemParameters.ResizeFrameVerticalBorderWidth;
            var captionHeight = SystemParameters.CaptionHeight;

            Width = snugContentWidth + 2 * verticalBorderWidth;
            Height = snugContentHeight + captionHeight + 2 * horizontalBorderHeight;
        }
    }
}

assuming a proportional page layout like (note no SizeToContent setting or Loaded event handler on the Window or Width and Height specified on the LayoutRoot):

<Window x:Class="WpfWindowBorderTest.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1">
    <Grid x:Name="LayoutRoot" Background="Green">
        <Grid.RowDefinitions>
            <RowDefinition Height="1*"/>
            <RowDefinition Height="3*"/>
        </Grid.RowDefinitions>
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="1*"/>
            <ColumnDefinition Width="3*"/>
        </Grid.ColumnDefinitions>
        <Rectangle Grid.Row="0" Grid.Column="0" Fill="Black" />
        <Rectangle Grid.Row="0" Grid.Column="0" Width="75" Height="75" Fill="Red" />
        <Rectangle Grid.Row="1" Grid.Column="1" Fill="Yellow" />
        <Rectangle Grid.Row="1" Grid.Column="1" Width="225" Height="225" Fill="Red" />
    </Grid>
</Window>

I haven't been able to come up with a way to do it declaratively in XAML as yet.

You can remove the window Width and Height attributes in XAML, and add SizeToContent="WidthAndHeight". This sets the initial dimensions of the window to its content, yet still lets you resize it.

<Window x:Class="WpfApplication2.Window1"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="Window1" SizeToContent="WidthAndHeight">
    <Grid>
        <TextBlock Text="How to set WPF window’s startup ClientSize?"/>
    </Grid>
</Window>

When started, it looks like this:

Yet you can still stretch it with the mouse:

I spend quite a time to figure that whole story too. It's surprisingly difficult to find a pure XAML (zero-code behind) answer to this question on the net, so here's mine.

When we design a Window in the Visual Studio WPF designer, the standard (and by default) way is to define Width and Height properties on the Window, like this in XAML:

<Window x:Class="WpfApplication1.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="75" Width="190">
    <Grid>
        <Button Content="Right" HorizontalAlignment="Right" Margin="0,0,10,10" VerticalAlignment="Bottom" Width="75" />
        <Button Content="Left" HorizontalAlignment="Left" Margin="10,0,0,10" VerticalAlignment="Bottom" Width="75"/>
    </Grid>
</Window>

The designer preview looks like this:

Everything looks cool, but when we run the application, depending on the current Windows version, theme and all display settings jazz, there are 99% chances that the runtime window will not look like the designed one. Here is what it looks on my Windows 8.1:

The initial solution is, like in Oren's answer to use the SizeTocontent property. It basically tells WPF to define the window size from it's content (aka "client size"), instead of the window itself (aka "client size + all that non-client/chrome/border totally incontrollable stuff").

So, we can define the Content to be of fixed size, like this:

<Window x:Class="WpfApplication1.MainWindowSizeToContentCentered"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" SizeToContent="WidthAndHeight">
    <Grid Height="40" Width="180">
        <Button Content="Right" HorizontalAlignment="Right" Margin="0,0,10,10" VerticalAlignment="Bottom" Width="75" />
        <Button Content="Left" HorizontalAlignment="Left" Margin="10,0,0,10" VerticalAlignment="Bottom" Width="75"/>
    </Grid>
</Window>

And now, the runtime window looks exactly how we want (Note the Grid's height and width don't have exactly the same values as the original Window one - 40/180 vs 75/190 -, and that's fine, as in design mode, you can now just forget window Height and Width property forever):

How does that behave when the window is resized? like this, the grid is centered, which is fine if you want that behavior:

But, if we want the behavior in the question, ("I can resize the window, but its content doesn't resize with it, because I specified a fixed size."), which was the original behavior too, instead of specifying Width and Height, we can use MinWidth and MinHeight, like this:

<Window x:Class="WpfApplication1.MainWindowSizeToContentResizable"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" SizeToContent="WidthAndHeight">
    <Grid MinHeight="40" MinWidth="180">
        <Button Content="Right" HorizontalAlignment="Right" Margin="0,0,10,10" VerticalAlignment="Bottom" Width="75" />
        <Button Content="Left" HorizontalAlignment="Left" Margin="10,0,0,10" VerticalAlignment="Bottom" Width="75"/>
    </Grid>
</Window>

The runtime window looks the same, but the resize experience is now comparable to the original default Window layout:

That should be the default WPF designer layout IMHO.