public class TypeSwitchConverter : Dictionary<Type, object>, IValueConverter
{
    public object Convert(object value, Type targetType, object parameter, .CultureInfo culture)
    {
        foreach (var mapping in this)
        {
            if (mapping.Key.IsAssignableFrom(value.GetType()))
            {
                return mapping.Value;
            }
        }

        return null;
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    {
        throw new NotImplementedException();
    }
}

<ListBox ItemsSource="{Binding}">
        <ListBox.ItemTemplate>
            <DataTemplate>
                <TextBlock Text="{Binding}">
                    <TextBlock.Style>
                        <Binding>
                            <Binding.Converter>
                                <my:TypeSwitchConverter>
                                    <Style x:Key="{x:Type cor:Int32}" TargetType="{x:Type TextBlock}">
                                        <Setter Property="Background" Value="Red" />
                                    </Style>
                                    <Style x:Key="{x:Type cor:String}" TargetType="{x:Type TextBlock}">
                                        <Setter Property="Background" Value="Green" />
                                    </Style>
                                    <Style x:Key="{x:Type sys:Uri}" TargetType="{x:Type TextBlock}">
                                        <Setter Property="Background" Value="Blue" />
                                    </Style>
                                </my:TypeSwitchConverter>
                            </Binding.Converter>
                        </Binding>
                    </TextBlock.Style>
                </TextBlock>
            </DataTemplate>
        </ListBox.ItemTemplate>
    </ListBox>