In order to add a Slider to the Home page of Magento it is not necessary to install an additional extension. A default Magento Slider can be used as well. In RWD Magento 1.9 there is a Slider plugin already added to jQuery library.
To create a custom Slider it is necessary to put HTML code of certain structure.
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For more information about Slider extension please follow the link.
A product slider for Magento you can find here.