How to remove default mouse-over effect on WPF buttons?

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.

<Style x:Key="SomeButtonStyle" TargetType="Button">
    <Setter Property="Background" Value="Transparent" />
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="Button">
                <Grid Background="{TemplateBinding Background}">
                    <ContentPresenter />
                </Grid>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
</Style>

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.

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>