Time Warner Cable - Internet Only Promo (YMMV)
The deals do not explicitly state new customers only. I was paying $54.99/mo for the Turbo internet and my own modem.
After a call to TWC (585-756-2000 for me), and a transfer to the Retention Dept, I was given the Extreme package for $44.99 for 12 months, fully anticipating they will jack up the rates a bit at the end.
Point being, if you have a lower package and paying the "standard" price, it won't hurt to give TWC a call and see if your price can be renegotiated.