I use a DataGridTemplateColumn to place an image of a trash can on every row of the grid. You could put a Button with an image as its content, instead of an Image in this example. When the user clicks on the image it will delete the row from the observable collection.
You will need to add
xmlns:i="clr-amespace:System.Windows.Interactivity;assembly=System.Windows.Interactivity"
xmlns:cmd="clr-namespace:GalaSoft.MvvmLight.Command;assembly=GalaSoft.MvvmLight.Platform" in order to use the interaction. But you can set the styles of the textblock, the cell and the image/button as in the Xaml below.
Hope this helps.
<DataGridTemplateColumn MinWidth="30" IsReadOnly="True">
<DataGridTemplateColumn.CellTemplate>
<DataTemplate>
<DataGridCell Style="{StaticResource YOURCellStyle}" >
<TextBlock Style="{StaticResource YOURTextBlockStyle}">
<Image Width="12"
Margin="0,0,0,0"
HorizontalAlignment="Center"
Source="pack://application:,,,/Resources/Images/DialogIcons/rubbish-bin.PNG"
Stretch="Uniform"
Style="{StaticResource YOURImageStyle}">
<i:Interaction.Triggers>
<i:EventTrigger EventName="MouseLeftButtonDown">
<cmd:EventToCommand Command="{Binding
Path=DataContext.YOURDeleteComand, ElementName=YOURDataGrid}"
CommandParameter="{Binding}"/>
</i:EventTrigger>
</i:Interaction.Triggers>
</Image>
</TextBlock>
</DataGridCell>
</DataTemplate>
</DataGridTemplateColumn.CellTemplate>
</DataGridTemplateColumn>
<Style x:Key="YourImageOrButtonStyle" TargetType="ImageOrButton">
<Setter Property="Cursor" Value="Hand"/>
<Setter Property="ToolTip" Value="Delete"/>
</Style>
<Style x:Key="YOURCellStyle" TargetType="DataGridCell">
<Setter Property="Background" Value="Transparent"/>
<Style.Triggers>
<Trigger Property="IsFocused" Value="True">
<Setter Property="Background" Value="Transparent"/>
<Setter Property="FocusVisualStyle" Value="{x:Null}"/>
</Trigger>
</Style.Triggers>
</Style>
<Style x:Key="YOURTextBlockStyle" TargetType="TextBlock">
<Setter Property="Background" Value="Transparent"/>
<Style.Triggers>
<Trigger Property="IsFocused" Value="True">
<Setter Property="Background" Value="Transparent"/>
<Setter Property="FocusVisualStyle" Value="{x:Null}"/>
</Trigger>
</Style.Triggers>
</Style>