This is similar to the solution referred by Mark Heath but with not as much code to just create a very basic button, without the built-in mouse over animation effect. It preserves a simple mouse over effect of showing the button border in black.
The style can be inserted into the Window.Resources or UserControl.Resources section for example (as shown).
<UserControl.Resources>
<!-- This style is used for buttons, to remove the WPF default 'animated' mouse over effect -->
<Style x:Key="MyButtonStyle" TargetType="Button">
<Setter Property="OverridesDefaultStyle" Value="True"/>
<Setter Property="Margin" Value="5"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="Button">
<Border Name="border"
BorderThickness="1"
Padding="4,2"
BorderBrush="DarkGray"
CornerRadius="3"
Background="{TemplateBinding Background}">
<ContentPresenter HorizontalAlignment="Center" VerticalAlignment="Center" />
</Border>
<ControlTemplate.Triggers>
<Trigger Property="IsMouseOver" Value="True">
<Setter TargetName="border" Property="BorderBrush" Value="Black" />
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
</UserControl.Resources>
<!-- usage in xaml -->
<Button Style="{StaticResource MyButtonStyle}">Hello!</Button>
If someone doesn't want to override default Control Template then here is the solution.
You can create DataTemplate for button which can have TextBlock and then you can write Property trigger on IsMouseOver property to disable mouse over effect. Height of TextBlock and Button should be same.
Just to add a very simple solution, that was good enough for me, and I think addresses the OP's issue. I used the solution in this answer except with a regular Background value instead of an image.
No re-templating beyond forcing the Background to always be the Transparent background from the templated button - mouseover no longer affects the background once this is done. Obviously replace Transparent with any preferred value.
The Muffin Man had a very simple answer which worked for me.
To add a little more specific direction, at least for VS 2013:
Right-click the control
Select Edit Template => Edit a copy...
I selected 'Application' for where to save the style
From here you can directly edit App.xaml and see the intuitively named properties. For my purposes, I just set RenderMouseOver="False"
Then, in the MainWindow.xaml or wherever your GUI is, you can paste the new style at the end of the Button tag, e.g. ... Style="{DynamicResource MouseOverNonDefault}"/>