WPF TreeView: How to style selected items with rounded corners like in Explorer

Add this into your TreeView.ContainerStyle to remove the default blue background.

<Style.Resources>
    <SolidColorBrush x:Key="{x:Static SystemColors.HighlightBrushKey}" Color="Transparent" />
    <SolidColorBrush x:Key="{x:Static SystemColors.ControlBrushKey}" Color="Transparent" />
    <SolidColorBrush x:Key="{x:Static SystemColors.HighlightTextBrushKey}" Color="Black" />
    <SolidColorBrush x:Key="{x:Static SystemColors.ControlTextBrushKey}" Color="Black" />
</Style.Resources>

You can replace the Black with whatever colour you want your item text and selected item text to be.

To have a grey background when not focused, you could set up a 'non focused' Style with a grey backgorund and use EventTriggers on the TreeViewItem.GotFocus and LostFocus events to switch between the Styles.

EDIT>>>

If you want to be flash, you can use animations to change between the background colours by adding triggers to your ItemBorder Border directly in your HierarchicalDataTemplate like so:

<Border.Triggers>
    <EventTrigger RoutedEvent="Border.GotFocus">
        <EventTrigger.Actions>
            <BeginStoryboard>
                <Storyboard>
                    <ColorAnimation Storyboard.TargetProperty="(Border.Background).(SolidColorBrush.Color)" To="YourColour" Duration="0:0:0.2" />
                </Storyboard>
            </BeginStoryboard>
        </EventTrigger.Actions>
    </EventTrigger>
    <EventTrigger RoutedEvent="Border.LostFocus">
        <EventTrigger.Actions>
            <BeginStoryboard>
                <Storyboard>
                    <ColorAnimation Storyboard.TargetProperty="(Border.Background).(SolidColorBrush.Color)" To="LightGray" Duration="0:0:0.2" />
                </Storyboard>
            </BeginStoryboard>
        </EventTrigger.Actions>
    </EventTrigger>
</Border.Triggers>

Note that this will only work if the ColorAnimation has a From colour. As this code stands, the runtime will look for a SolidColorBrush set on the Border.Background property, so you must set one. You could set the ColorAnimation.From property directly instead.

Adding to @Sheridan's answer
This isn't a 100% accurate but should get you pretty close (it's using the colors from GridView which is pretty close to Windows Explorer)

<TreeView ...>
    <TreeView.Resources>
        <LinearGradientBrush x:Key="{x:Static SystemColors.HighlightBrushKey}" EndPoint="0,1" StartPoint="0,0">
            <GradientStop Color="#FFD9F4FF" Offset="0"/>
            <GradientStop Color="#FF9BDDFB" Offset="1"/>
        </LinearGradientBrush>
        <LinearGradientBrush x:Key="{x:Static SystemColors.ControlBrushKey}" EndPoint="0,1" StartPoint="0,0">
            <GradientStop Color="#FFEEEDED" Offset="0"/>
            <GradientStop Color="#FFDDDDDD" Offset="1"/>
        </LinearGradientBrush>
        <SolidColorBrush x:Key="{x:Static SystemColors.HighlightTextBrushKey}" Color="Black" />
        <SolidColorBrush x:Key="{x:Static SystemColors.ControlTextBrushKey}" Color="Black" />
    </TreeView.Resources>
    <TreeView.ItemContainerStyle>
        <Style TargetType="{x:Type TreeViewItem}">
            <Setter Property="BorderThickness" Value="1.5"/>
            <Style.Triggers>
                <Trigger Property="IsSelected" Value="True">
                    <Setter Property="BorderBrush" Value="#adc6e5"/>
                </Trigger>
                <MultiTrigger>
                    <MultiTrigger.Conditions>
                        <Condition Property="IsSelected" Value="True"/>
                        <Condition Property="IsSelectionActive" Value="False"/>
                    </MultiTrigger.Conditions>
                    <Setter Property="BorderBrush" Value="LightGray"/>
                </MultiTrigger>
            </Style.Triggers>
            <Style.Resources>
                <Style TargetType="Border">
                    <Setter Property="CornerRadius" Value="2"/>
                </Style>
            </Style.Resources>                    
        </Style>
    </TreeView.ItemContainerStyle>
</TreeView>