How to perform Single click checkbox selection in WPF DataGrid?

For single click DataGrid checkbox you can just put regular checkbox control inside DataGridTemplateColumn and set UpdateSourceTrigger=PropertyChanged.

<DataGridTemplateColumn.CellTemplate>
    <DataTemplate>
        <CheckBox IsChecked="{Binding Path=IsSelected, UpdateSourceTrigger=PropertyChanged}" />
    </DataTemplate>
</DataGridTemplateColumn.CellTemplate>

I solved this with the following Style:

<Style TargetType="DataGridCell">
     <Style.Triggers>
         <Trigger Property="IsMouseOver" Value="True">
             <Setter Property="IsEditing" Value="True" />
         </Trigger>
     </Style.Triggers>
 </Style>

It's of course possible to adapt this further for specific columns ...

First of, I know this is a pretty old question but I still thought I'd try and answer it.

I had the same problem a couple of days ago and came across a surprisingly short solution for it (see this blog). Basically, all you need to do is replace the DataGridCheckBoxColumn definition in your XAML with the following:

<DataGridTemplateColumn Header="MyCheckBoxColumnHeader">
    <DataGridTemplateColumn.CellTemplate>
        <DataTemplate>
            <CheckBox HorizontalAlignment="Center" VerticalAlignment="Center" IsChecked="{Binding Path=MyViewModelProperty, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" />
        </DataTemplate>
    </DataGridTemplateColumn.CellTemplate>
</DataGridTemplateColumn>

The upside of this solution is obvious - it's XAML-only; thus it effectively refrains your from burdening your code-behind with additional UI logic.