This is how you do it.
First thing, create a style element in your ResourceDictionary or if you don't have one drop it on the page itself:
<Style x:Key="alternatingListViewItemStyle" TargetType="{x:Type ListViewItem}">
<Style.Triggers>
<!-- setting up triggers for alternate background colors -->
<Trigger Property="ItemsControl.AlternationIndex" Value="1">
<Setter Property="Background" Value="LightGray"></Setter>
</Trigger>
<Trigger Property="ItemsControl.AlternationIndex" Value="2">
<Setter Property="Background" Value="White"></Setter>
</Trigger>
</Style.Triggers>
<!-- setting row height here -->
<Setter Property="Height" Value="30" />
</Style>
Now set the ItemContanerStyle on the actual ListView and set the AlternationCount attribute):
<ListView Name="recordContainer" ItemContainerStyle="{StaticResource alternatingListViewItemStyle}" AlternationCount="2" >
<ListView.View>
<GridView>
<!-- Just a few sample columns -->
<GridViewColumn Header="aField" />
<GridViewColumn Header="anotherField" />
<GridViewColumn Header="yetAnotherField" />
</GridView>
</ListView.View>
<!-- Whatever you might have in here -->
</ListView>
And this is all there is to it!