If a live wire contacts the bare copper pipe, and it's not grounded, it can kill you if you touch the pipe or a faucet.
Plumbers have died working on ungrounded copper pipes.
Correction below by jwelectric
No, it is not so important to ground the pipe as it is to ensure it is bonded. If the home has a water heater then the pipe is bonded through the equipment grounding conductor in the branch circuit supplying the water heater. If there is anyone who thinks this would not bond the metal water pipes then none of the pipes would require bonding. If the metal water piping system is mixed with nonmetallic fittings or anything else that would break the continuity then no bonding is required and again trying to ground the pipes could prove to be deadly.