This likely only works if you have the Triple Play package, but if you're an existing CV customer for any of their services its worth a shot.
My bill with CV was $157.65/month for their basic cable TV package (including DVR on 2 TVs), basic internet, and home phone. I called DirecTV and Verizon and scheduled them to come install their services for 2 weeks down the road. I then called CV and asked them to cancel my service. When I told them I was cancelling due to switching services, they transferred me to the retention department. The retention rep tried every trick in the book to convince me to stay, including inventing blatantly false stories about DTV service going down weekly for her grandma, Verizon internet going down often for her brother etc.
Ultimately she ended up giving me a better cable package, the fastest internet they have (I've gotten 54mbps plugged in and 28mbps on wifi), and an upgraded calling plan for the grand total of $88.85/month for the next 12 months.
All I had to do was forward her my confirmation emails from DTV and Verizon. I then called DTV and Verizon and cancelled my appointments with them. Took a total of approximately 1 hour for the entire job. I'm going to save over $800 over the course of the year, so I'd definitely recommend trying.