Disable DataGrid current cell border in FullRow selection mode

You could set the BorderThickness for DataGridCell to 0

<DataGrid ...          SelectionUnit="FullRow">    <DataGrid.CellStyle>        <Style TargetType="DataGridCell">            <Setter Property="BorderThickness" Value="0"/>            <!-- Update from comments.                 Remove the focus indication for the selected cell -->            <Setter Property="FocusVisualStyle" Value="{x:Null}"/>        </Style>    </DataGrid.CellStyle>    <!-- ... --></DataGrid>

Saw another answer here that was close, but it didn't get rid of the Focus rectangle. Here's how to obliterate all of the borders.

<DataGrid.Resources>    <Style TargetType="{x:Type DataGridCell}">        <Setter Property="BorderThickness" Value="0" />        <Setter Property="FocusVisualStyle" Value="{x:Null}" />    </Style></DataGrid.Resources>

Also, since technically those cells still do get focus (you just don't see it), to make the tab key advance to the next row instead of the next cell, I define a cell style based on the above but which also adds the following...

<DataGrid.Resources>    <Style x:Key="NoFocusDataGridCell" TargetType="{x:Type DataGridCell}" BasedOn="{StaticResource {x:Type DataGridCell}}">        <Setter Property="Focusable"        Value="False" />        <Setter Property="IsTabStop"        Value="False" />        <Setter Property="IsHitTestVisible" Value="False" />    </Style></DataGrid.Resources>

...then I apply that to all but the first column definition. That way the tab key advances to the next row, not the next cell.

Back to the borders however. If you want to hide them but still want them to be part of the layout for spacing-reasons, change the above to this...

<DataGrid.Resources>    <Style TargetType="{x:Type DataGridCell}">        <Setter Property="BorderBrush" Value="Transparent" />        <Setter Property="FocusVisualStyle" Value="{x:Null}" />    </Style></DataGrid.Resources>

Enjoy! :)

<Style x:Key="DataGrid" TargetType="DataGrid">    <Setter Property="CellStyle">        <Setter.Value>            <Style TargetType="DataGridCell">                <Setter Property="BorderThickness" Value="0"/>                <Setter Property="Foreground" Value="{Binding Foreground, RelativeSource={RelativeSource TemplatedParent}}" />                <Setter Property="Background" Value="{Binding Background, RelativeSource={RelativeSource TemplatedParent}}" />            </Style>        </Setter.Value>    </Setter></Style>