There are a number of ways you can customize the look & feel of your tooltips:
To change the overall look and feel of the tooltip, set the Skin property.
To change the way the tooltip initially becomes visible, use the Animation property.
To change the look of an individual aspect of the tooltip, use its CssClass property and set up CSS rules as needed.
To change the initial position of the tooltip use the Position property which is an enumerator.
Since Q1 2012 the shadow is enabled by default. You can control it via the EnableShadow property.