That's a great question and the answer is generally no, you shouldn't have to purchase any more cables for normal hook up. However depending on the cabling you currently have and how you want to hook up the Slingbox, you may. If you plan to use the pass-through function of the Slingbox (to the TV), and as long as you already have component and HDMI cables from your cable box to your TV then you wouldn't need any additional cables.
Here are a couple of articles with more information regarding your inquiry:
Hope this helps!
The Sling Moderation Team