Use a DataTrigger
:
<DataGrid ItemsSource="{Binding YourItemsSource}">
<DataGrid.RowStyle>
<Style TargetType="DataGridRow">
<Style.Triggers>
<DataTrigger Binding="{Binding State}" Value="State1">
<Setter Property="Background" Value="Red"></Setter>
</DataTrigger>
<DataTrigger Binding="{Binding State}" Value="State2">
<Setter Property="Background" Value="Green"></Setter>
</DataTrigger>
</Style.Triggers>
</Style>
</DataGrid.RowStyle>
</DataGrid>