Hide Tab headers in WPF TabControl

You can use a Style applied to TabItem with a DataTrigger that will collapse it if the parent TabControl has only one item:

<Grid xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
      xmlns:sys="clr-namespace:System;assembly=mscorlib"
      xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
    <Grid.Resources>
        <x:Array x:Key="tabData" Type="{x:Type sys:String}">
            <sys:String>do</sys:String>
            <sys:String>re</sys:String>
            <sys:String>mi</sys:String>
        </x:Array>
    </Grid.Resources>
    <TabControl ItemsSource="{StaticResource tabData}">
        <TabControl.ItemContainerStyle>
            <Style TargetType="{x:Type TabItem}">
                <Style.Triggers>
                    <DataTrigger Binding="{Binding RelativeSource={RelativeSource Mode=FindAncestor, AncestorType={x:Type TabControl}}, Path=Items.Count}" Value="1">
                        <Setter Property="Visibility" Value="Collapsed"/>
                    </DataTrigger>
                </Style.Triggers>                
            </Style>
        </TabControl.ItemContainerStyle>
    </TabControl>
</Grid>

If you want to get rid of the TabControl completely if there is only one item, that logic should probably be at a higher level.

And if you have to do it in code behind....

foreach (var item in tabControl.Items)
            (item as TabItem).Visibility = tabControl.Items.Count > 1 ? Visibility.Visible : Visibility.Collapsed;