Gaps between items in my ListBox

This is because of the padding inside the default ItemContainerStyle for ListBoxItem. To remove this you can override the ItemContainerStyle. For example just try the below Empty ItemContainerStyle to your ListBox and you can see the margin is no more.

    <ListBox >
        <ListBox.ItemsPanel>
            <ItemsPanelTemplate >
                <VirtualizingStackPanel IsItemsHost="True" Orientation="Horizontal"/>
            </ItemsPanelTemplate>
        </ListBox.ItemsPanel>
        <ListBox.ItemContainerStyle>
            <Style TargetType="{x:Type ListBoxItem}">
                <Setter Property="Template">
                    <Setter.Value>
                        <ControlTemplate TargetType="{x:Type ListBoxItem}">
                            <ContentPresenter/>
                        </ControlTemplate>
                    </Setter.Value>
                </Setter>
            </Style>
        </ListBox.ItemContainerStyle>
        <Button Content="hello1" Width="75"/>
        <Button Content="Hello2" Width="75"/>
    </ListBox>