WPF: switching UserControls depending on corresponding ViewModels (MVVM)

Is it possible to deduce the necessary user control based on a ViewModel type?

You mean, like this?

<Window.Resources>
   <DataTemplate DataType="{x:Type vm:LionViewModel}">
      <v:LionView />
   </DataTemplate>
   <DataTemplate DataType="{x:Type vm:SnakeViewModel}">
      <v:SnakeView />
   </DataTemplate>
   <DataTemplate DataType="{x:Type vm:BirdViewModel}">
      <v:BirdView/>
   </DataTemplate>
</Window.Resources>

See "Applying a View to a View Model" in Josh Smith's article on MVVM.

Edit:

Here's a trivial example of type-based template selection that you can paste into Kaxaml to prove to yourself that it really works:

<Page
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  xmlns:sys="clr-namespace:System;assembly=mscorlib">
  <Page.Resources>
    <sys:String x:Key="string">this is a string</sys:String>
    <sys:Int32 x:Key="int32">1234</sys:Int32>
    <DataTemplate DataType="{x:Type sys:String}">
      <TextBlock Foreground="Red" Text="{Binding}"/>
    </DataTemplate>
    <DataTemplate DataType="{x:Type sys:Int32}">
      <TextBlock Foreground="Blue" Text="{Binding}"/>
    </DataTemplate>
  </Page.Resources>
  <StackPanel>  
    <ContentControl Content="{Binding Source={StaticResource string}}"/>
    <ContentControl Content="{Binding Source={StaticResource int32}}"/>
  </StackPanel>
</Page>

You can use DataTemplateSelector for that. The method of choosing the right template is up to you. You can use enums or test for class type if you wish.