XAML:

<Window x:Class="WpfApplication2.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525">
    <Grid>
        <TextBox x:Name="t1" HorizontalAlignment="Left" Height="23" Margin="101,43,0,0" TextWrapping="Wrap" Text="TextBox" VerticalAlignment="Top" Width="120"/>
        <TextBox x:Name="t2" HorizontalAlignment="Left" Height="23" Margin="101,91,0,0" TextWrapping="Wrap" Text="TextBox" VerticalAlignment="Top" Width="120"/>
    </Grid>
</Window>

Code:

        public MainWindow()
        {
            InitializeComponent();
            Binding binding = new Binding();
            binding.Source = t1; 
            binding.Path = new PropertyPath(TextBox.TextProperty);
            BindingOperations.SetBinding(t2, TextBox.TextProperty, binding);
        }