If simply put that your ItemsSource is bound like this:
YourListBox.ItemsSource = new List<String> { "One", "Two", "Three" };
Your XAML should look like:
<ListBox Margin="20" Name="YourListBox">
    <ListBox.ItemTemplate> 
        <DataTemplate> 
            <StackPanel Orientation="Horizontal"> 
                <TextBlock Text="{Binding}" /> 
            </StackPanel> 
        </DataTemplate> 
    </ListBox.ItemTemplate> 
</ListBox> 
Update:
This is a solution when using a DataContext. Following code is the viewmodel you will be passing to the DataContext of the page and the setting of the DataContext:
public class MyViewModel
{
    public List<String> Items
    {
        get { return new List<String> { "One", "Two", "Three" }; }
    }
}
//This can be done in the Loaded event of the page:
DataContext = new MyViewModel();
Your XAML now looks like this:
<ListBox Margin="20" ItemsSource="{Binding Items}">
    <ListBox.ItemTemplate>
        <DataTemplate>
            <StackPanel Orientation="Horizontal">
                <TextBlock Text="{Binding}" />
            </StackPanel>
        </DataTemplate>
    </ListBox.ItemTemplate>
</ListBox>
The advantage of this approach is that you can put a lot more properties or complex objects in the MyViewModel class and extract them in the XAML. For example to pass a List of Person objects:
public class ViewModel
{
    public List<Person> Items
    {
        get
        {
            return new List<Person>
            {
                new Person { Name = "P1", Age = 1 },
                new Person { Name = "P2", Age = 2 }
            };
        }
    }
}
public class Person
{
    public string Name { get; set; }
    public int Age { get; set; }
}
And the XAML:
<ListBox Margin="20" ItemsSource="{Binding Items}">
    <ListBox.ItemTemplate>
        <DataTemplate>
            <StackPanel Orientation="Horizontal">
                <TextBlock Text="{Binding Path=Name}" />
                <TextBlock Text="{Binding Path=Age}" />
            </StackPanel>
        </DataTemplate>
    </ListBox.ItemTemplate>
</ListBox>