wpf flat button

More simple solution here using already defined ToolBar button style :

<Button Style="{StaticResource {x:Static ToolBar.ButtonStyleKey}}"
        Content="You know I'm flat..." />

Just to get you started:

<Page
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
  <Page.Resources>
    <Style x:Key="Flat">
        <Setter Property="Control.Background" Value="{x:Null}" />
        <Setter Property="Control.BorderBrush" Value="{x:Null}" />
        <Style.Triggers>
            <Trigger Property="Control.IsMouseOver" Value="True">
                <Setter Property="Control.Background" Value="{x:Null}" />
                <Setter Property="Control.BorderBrush" Value="{x:Null}" />
                <Setter Property="Control.FontWeight" Value="Bold" />
            </Trigger>
            <Trigger Property="Control.IsFocused" Value="True">
                <Setter Property="Control.FontWeight" Value="Bold" />
            </Trigger>
        </Style.Triggers>
    </Style>
  </Page.Resources>
  <StackPanel>  
    <Button Style="{StaticResource Flat}">Hello</Button>
  </StackPanel>
</Page>

Then you have one millon other ways to do it, even changing the ControlTemplate to complete redefine the Button

To add to Eduardo's answer, this solution gets rid of any extra styling such as the border around the button if the thickness is set to 0.

You can add extra styling as needed:

<Style x:Key="Flat" TargetType="Button">
    <Setter Property="Background" Value="{x:Null}" />
    <Setter Property="BorderBrush" Value="{x:Null}" />
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="{x:Type Button}">
                <Border BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderThickness}" Padding="{TemplateBinding Padding}">
                    <ContentPresenter HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}" Margin="{TemplateBinding Padding}" RecognizesAccessKey="True" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" VerticalAlignment="{TemplateBinding VerticalContentAlignment}"/>
                </Border>
                <ControlTemplate.Triggers>
                    <Trigger Property="IsKeyboardFocused" Value="true">
                    </Trigger>
                    <Trigger Property="IsDefaulted" Value="true">
                    </Trigger>
                    <Trigger Property="IsPressed" Value="true">
                    </Trigger>
                    <Trigger Property="ToggleButton.IsChecked" Value="true">
                    </Trigger>
                    <Trigger Property="IsEnabled" Value="false">
                        <Setter Property="Foreground" Value="{DynamicResource {x:Static SystemColors.GrayTextBrushKey}}"/>
                    </Trigger>
                </ControlTemplate.Triggers>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
    <Style.Triggers>
        <Trigger Property="IsMouseOver" Value="True">
            <Setter Property="Background" Value="{x:Null}" />
            <Setter Property="BorderBrush" Value="{x:Null}" />
            <Setter Property="FontWeight" Value="Normal" />
        </Trigger>
        <Trigger Property="IsFocused" Value="True">
            <Setter Property="FontWeight" Value="Normal" />
        </Trigger>
    </Style.Triggers>
</Style>