WPF ListView turn off selection

Set the style of each ListViewItem to have Focusable set to false.

<ListView ItemsSource="{Binding Test}" >
    <ListView.ItemContainerStyle>
        <Style TargetType="{x:Type ListViewItem}">
            <Setter Property="Focusable" Value="False"/>
        </Style>
    </ListView.ItemContainerStyle>
</ListView>

Moore's answer doesn't work, and the page here:

Specifying the Selection Color, Content Alignment, and Background Color for items in a ListBox

explains why it cannot work.

If your listview only contains basic text, the simplest way to solve the problem is by using transparent brushes.

<Window.Resources>
  <Style TargetType="{x:Type ListViewItem}">
    <Style.Resources>
      <SolidColorBrush x:Key="{x:Static SystemColors.HighlightBrushKey}" Color="#00000000"/>
      <SolidColorBrush x:Key="{x:Static SystemColors.ControlBrushKey}" Color="#00000000"/>
    </Style.Resources>
  </Style>
</Window.Resources>

This will produce undesirable results if the listview's cells are holding controls such as comboboxes, since it also changes their color. To solve this problem, you must redefine the control's template.

  <Window.Resources>
    <Style TargetType="{x:Type ListViewItem}">
      <Setter Property="Template">
        <Setter.Value>
          <ControlTemplate TargetType="{x:Type ListViewItem}">
            <Border SnapsToDevicePixels="True" 
                    x:Name="Bd" 
                    Background="{TemplateBinding Background}" 
                    BorderBrush="{TemplateBinding BorderBrush}" 
                    BorderThickness="{TemplateBinding BorderThickness}" 
                    Padding="{TemplateBinding Padding}">
              <GridViewRowPresenter SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" 
                                    VerticalAlignment="{TemplateBinding VerticalContentAlignment}" 
                                    Columns="{TemplateBinding GridView.ColumnCollection}" 
                                    Content="{TemplateBinding Content}"/>
            </Border>
            <ControlTemplate.Triggers>
              <Trigger Property="IsEnabled" 
                       Value="False">
                <Setter Property="Foreground" 
                        Value="{DynamicResource {x:Static SystemColors.GrayTextBrushKey}}"/>
              </Trigger>
            </ControlTemplate.Triggers>
          </ControlTemplate>
        </Setter.Value>
      </Setter>
    </Style>
  </Window.Resources>

Per Martin Konicek's comment, to fully disable the selection of the items in the simplest manner:

<ListView>
    <ListView.ItemContainerStyle>
        <Style TargetType="ListViewItem">
            <Setter Property="Focusable" Value="false"/>
        </Style>
    </ListView.ItemContainerStyle>
    ...
</ListView>

However if you still require the functionality of the ListView, like being able to select an item, then you can visually disable the styling of the selected item like so:

You can do this a number of ways, from changing the ListViewItem's ControlTemplate to just setting a style (much easier). You can create a style for the ListViewItems using the ItemContainerStyle and 'turn off' the background and border brush when it is selected.

<ListView>
    <ListView.ItemContainerStyle>
        <Style TargetType="{x:Type ListViewItem}">
            <Style.Triggers>
                <Trigger Property="IsSelected"
                         Value="True">
                    <Setter Property="Background"
                            Value="{x:Null}" />
                    <Setter Property="BorderBrush"
                            Value="{x:Null}" />
                </Trigger>
            </Style.Triggers>
        </Style>
    </ListView.ItemContainerStyle>
    ...
</ListView>

Also, unless you have some other way of notifying the user when the item is selected (or just for testing) you can add a column to represent the value:

<GridViewColumn Header="IsSelected"
                DisplayMemberBinding="{Binding RelativeSource={RelativeSource Mode=FindAncestor, AncestorType={x:Type ListViewItem}}, Path=IsSelected}" />