You don't need cable TV service, but you DO need a video cable to connect the Wii to your TV. The Wii lacks HDMI (except Wii U). Here are your options ranked by quality.
Wii outputs stereo only. For surround, use your TV/Receiver's Pro Logic II decoding on the analog L/R.
Bottom Line: Buy a Component cable if your TV has Red/Blue/Green inputs. Otherwise, Wii2HDMI is the cheap modern fix.