if you just want the default style then
<TextBox Style="{x:Null}"/>
otherwise Cédric Bignon's answer with target type defined (like below) will do the job. No property will be inherited by your application TextBoxStyle
<TextBox>
<TextBox.Style>
<Style TargetType="{x:Type TextBox}">
<!-- your setters-->
</Style>
</TextBox.Style>
</TextBox>
if you want to slightly change the default application style then use the following tecqnique where in your style you can redefine properties you want to be different from the default or define additional ones
<TextBox>
<TextBox.Style>
<Style TargetType="{x:Type TextBox}" BasedOn="{StaticResource {x:Type TextBox}}">
<!-- your setters-->
</Style>
</TextBox.Style>
</TextBox>