Forcing a WPF tooltip to stay on the screen

If you want to set this for just one tooltip, set the duration on the object having the Tooltip, like this:

<Label ToolTipService.ShowDuration="12000" Name="lblShowTooltip" Content="Shows tooltip">
    <Label.ToolTip>
        <ToolTip>
            <TextBlock>Hello world!</TextBlock>
        </ToolTip>
    </Label.ToolTip>
</Label>

I'd say that this design was chosen because it allows same tooltip with different timeouts on different controls.

If you want this globally for your whole app, see the accepted answer.

Just put this code in initialization section.

ToolTipService.ShowDurationProperty.OverrideMetadata(
    typeof(DependencyObject), new FrameworkPropertyMetadata(Int32.MaxValue));