Often we have clients for whom we are developing a theme who request that they have several different block styles to choose from. Sometimes each style is completely different (colors, borders, images) while other times it is something as subtle as a different header icon.
A quick way of letting the site admin quickly change a block's style is with the Block Class module. It adds a "CSS Class(es)" text field to each Block's configuration page. The site admin then only needs to type in the pre-determined class names to achieve a desired look.
One of the nice features of this module is the fact that the site admin can add multiple CSS classes. This then allows them to add classes like, "green globeicon whitebg". By providing the client with a set of classes they can mix and match, you've given them complete control and flexibility over their block displays.