Hide the TabControl header

Actually, it's very straight forward to hide the tab strip. You just set each TabItems Visibility to Collapsed. You still see the tab content,...just not the tab header itself.

Simple XAML Style

<TabControl>
    <TabControl.ItemContainerStyle>
        <Style TargetType="{x:Type TabItem}">
            <Setter Property="Visibility" Value="Collapsed"/>
        </Style>
    </TabControl.ItemContainerStyle>
    ...
</TabControl>

Well, there are several ways to do this.

The ugliest way: Use VisualTreeHelper to find TabPanel (or any other Panel you use to host items), and set it's Visibility property to Visibility.Collapsed. Why ugly? It's easy to create few annoying bugs here or break this approach with 'harmless' style update if you was not careful enough...

I prefer using combination of Xaml and code behind. You bind either TabItem's visibility to view model property or TabPanel's visibility to view model property. In both cases you have to override style (either ItemContainer's style or whole TabControl's style). In both cases you have view model. Now, to toggle tab header's visibility, you just update a property in the view model. Here is an example with TabItems:

XAML

<Window x:Class="WpfApplication5.Window1"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:local="clr-namespace:WpfApplication5"
        Title="Tab Settings"
        Height="300"
        Width="300">
  <Window.Resources>
    <local:TabControlViewModel x:Key="tabVM" />
    <BooleanToVisibilityConverter x:Key="booleanToVisibilityConverter" />
  </Window.Resources>
  <Grid>
    <TabControl DataContext="{StaticResource tabVM}">
      <TabControl.ItemContainerStyle>
        <Style TargetType="{x:Type TabItem}">
          <Setter Property="Visibility"
                  Value="{Binding TabHeaderVisible, Converter={StaticResource booleanToVisibilityConverter}}" />
        </Style>
      </TabControl.ItemContainerStyle>
      <TabItem Header="Tab 1">
        <StackPanel>
          <TextBlock Text="Content" />
          <Button Content="Toggle Header"
                  Click="ToggleHeaderClick" />
        </StackPanel>
      </TabItem>
      <TabItem Header="Tab 2 Header">
        <TextBlock Text="Tab 2 Content" />
      </TabItem>
    </TabControl>
  </Grid>
</Window>

C#

using System.ComponentModel;
using System.Windows;
using System.Windows.Input;

namespace WpfApplication5
{
  public partial class Window1 : Window
  {
    public Window1()
    {
      InitializeComponent();
    }

    private void ToggleHeaderClick(object sender, RoutedEventArgs e)
    {
      var tabControlVM =
        ((FrameworkElement)sender).DataContext as TabControlViewModel;
      if (tabControlVM != null)
      {
        tabControlVM.TabHeaderVisible = !tabControlVM.TabHeaderVisible;
      }
    }
  }

  public class TabControlViewModel : INotifyPropertyChanged
  {
    private bool _tabHeaderVisible = true;

    public ICommand ToggleHeader
    {
      get; private set;
    }

    public bool TabHeaderVisible
    {
      get { return _tabHeaderVisible; }
      set
      {
        _tabHeaderVisible = value;
        OnPropertyChanged("TabHeaderVisible");
      }
    }

    public event PropertyChangedEventHandler PropertyChanged;

    private void OnPropertyChanged(string name)
    {
      var changed = PropertyChanged;
      if (changed != null)
      {
        changed(this, new PropertyChangedEventArgs(name));
      }
    }
  }
}

Style s = new Style();
s.Setters.Add(new Setter(UIElement.VisibilityProperty, Visibility.Collapsed));
tabControl.ItemContainerStyle = s;