Can I specify a generic type in XAML (pre .NET 4 Framework)?

Not directly in XAML, however you could reference a DataTemplateSelector from XAML to choose the correct template.

public class CustomerTemplateSelector : DataTemplateSelector
{
    public override DataTemplate SelectTemplate(object item,
                                                DependencyObject container)
    {
        DataTemplate template = null;
        if (item != null)
        {
            FrameworkElement element = container as FrameworkElement;
            if (element != null)
            {
                string templateName = item is ObservableCollection<MyCustomer> ?
                    "MyCustomerTemplate" : "YourCustomerTemplate";

                template = element.FindResource(templateName) as DataTemplate;
            } 
        }
        return template;
    }
}

public class MyCustomer
{
    public string CustomerName { get; set; }
}

public class YourCustomer
{
    public string CustomerName { get; set; }
}

The resource dictionary:

<ResourceDictionary 
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="clr-namespace:WpfApplication1"
    >
    <DataTemplate x:Key="MyCustomerTemplate">
        <Grid>
            <Grid.RowDefinitions>
                <RowDefinition Height="Auto"/>
                <RowDefinition Height="150"/>
            </Grid.RowDefinitions>
            <TextBlock Text="My Customer Template"/>
            <ListBox ItemsSource="{Binding}"
                     DisplayMemberPath="CustomerName"
                     Grid.Row="1"/>
        </Grid>
    </DataTemplate>

    <DataTemplate x:Key="YourCustomerTemplate">
        <Grid>
            <Grid.RowDefinitions>
                <RowDefinition Height="Auto"/>
                <RowDefinition Height="150"/>
            </Grid.RowDefinitions>
            <TextBlock Text="Your Customer Template"/>
            <ListBox ItemsSource="{Binding}"
                     DisplayMemberPath="CustomerName"
                     Grid.Row="1"/>
        </Grid>
    </DataTemplate>
</ResourceDictionary>

The window XAML:

<Window 
    x:Class="WpfApplication1.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1" 
    Height="300" 
    Width="300"
    xmlns:local="clr-namespace:WpfApplication1"
    >
    <Grid>
        <Grid.Resources>
            <local:CustomerTemplateSelector x:Key="templateSelector"/>
        </Grid.Resources>
        <ContentControl 
            Content="{Binding}" 
            ContentTemplateSelector="{StaticResource templateSelector}" 
            />
    </Grid>
</Window>

The window code behind:

public partial class Window1
{
    public Window1()
    {
        InitializeComponent();
        ObservableCollection<MyCustomer> myCustomers
            = new ObservableCollection<MyCustomer>()
        {
            new MyCustomer(){CustomerName="Paul"},
            new MyCustomer(){CustomerName="John"},
            new MyCustomer(){CustomerName="Mary"}
        };

        ObservableCollection<YourCustomer> yourCustomers
            = new ObservableCollection<YourCustomer>()
        {
            new YourCustomer(){CustomerName="Peter"},
            new YourCustomer(){CustomerName="Chris"},
            new YourCustomer(){CustomerName="Jan"}
        };
        //DataContext = myCustomers;
        DataContext = yourCustomers;
    }
}

Not out of the box, no; but there are enterprising developers out there who have done so.

Mike Hillberg at Microsoft played with it in this post, for example. Google has others of course.

You also can wrap your generic class in a derived class that specifies the T

public class StringList : List<String>{}

and use StringList from XAML.