In a lot of instances, depending on the name of our businesses, slogans can be used to clarify what we do and who we do it for. Take "Call that girl" for example. Why call that girl? Call that girl for what? A date? Fashion advice? No, her slogans make it pretty clear: "Call That Girl, We are here to help"
In other situations, you can use a slogan to further identify with and sell your customers on *why* they should call you, as evidenced by the "hometown" post above by Roborob.
So is it as important as a logo? Could be, depending on your business name and how that name appeals to your current target market.