<ListBox x:Name="ListBox1" SelectionMode="Multiple" Margin="10,10,357,20" ItemsSource="{Binding Items}">
    <ListBox.ItemTemplate>
        <DataTemplate>
            <StackPanel Orientation="Horizontal">
                <CheckBox Content="{Binding}" IsChecked="False"/>
            </StackPanel>
        </DataTemplate>
    </ListBox.ItemTemplate>
</ListBox>

private void Button1_Click(object sender, RoutedEventArgs e)
    {
        listOfNumbers = new List<int>();
        listOfNumbers.Add(1);
        listOfNumbers.Add(5);
        listOfNumbers.Add(34);

        ListBox1.ItemsSource = listOfNumbers;
    }

class IntWithChoiceVM : DependencyObject
{
    public int Value
    {
        get { return (int)GetValue(ValueProperty); }
        set { SetValue(ValueProperty, value); }
    }

    public static readonly DependencyProperty ValueProperty =
        DependencyProperty.Register(
                "Value", typeof(int), typeof(IntWithChoiceVM));

    public bool IsSelected
    {
        get { return (bool)GetValue(IsSelectedProperty); }
        set { SetValue(IsSelectedProperty, value); }
    }

    public static readonly DependencyProperty IsSelectedProperty =
        DependencyProperty.Register(
                 "IsSelected", typeof(bool), typeof(IntWithChoiceVM));
}

class ListChoiceVM : DependencyObject
{
    public ListChoiceVM(List<int> initial)
    {
        Values = new ObservableCollection();
        foreach (var n in initial)
            Values.Add(new IntWithChoiceVM() { Value = n, IsSelected = true });
    }

    public ObservableCollection<IntWithChoiceVM> Values { get; private set; }

    public IEnumerable<int> GetSelectedInts()
    {
        return Values.Where(v => v.IsSelected).Select(v => v.Value);
    }
}

<ListBox SelectionMode="Multiple" ItemsSource="{Binding Values}">
    <ListBox.ItemTemplate>
        <DataTemplate>
                <CheckBox Content="{Binding Value}"
                          IsChecked="{Binding IsSelected}"/>
        </DataTemplate>
    </ListBox.ItemTemplate>
</ListBox>