Since moving to a new apartment, I've no longer had cable TV. (at the last apartment basic cable was included) So far my girlfriend and I are getting by with Netflix. I think it's a great alternative to cable TV. We're on the "4 at a time" plan which cost about $25 a month, a lot less than cable. Netflix has a lot of TV series and since we don't watch a lot of TV to begin with, we havn't seen all of the shows yet
We're renting shows like Grey's anatomy, Veronica Mars, Futurama etc.
To do what you want to do, it's pretty complicated, but certainly can be done if you're technologically inclined. (and if you do get CC working well please post again because getting CC to work will be the hardest part)
For the most part, Vampyrox is right. you <i>could</i> get hit with a lawsuit and charged with DMCA violation, but you could also get hit with "theft of service" (cable TV) which may or may not be more or less likely. Here's the thing:
Let's imagine you are getting cable TV, if you set up a way to let you watch the cable TV on your computer at school or work, or on vacation, that would be ok. but if you set it up so that you could watch cable TV that's in your friend's house, and you don't have cable TV yourself, that's bad.
That being said let's take a look at what you'd need to do.
There are products like slingbox and Hava that do exactly what you're talking about. They're set-top boxes that stream video over the internet. The big problem is that they don't support closed captioning. You'd have to get a CC decoder and hook it up that way. (There is a software alternative that's free called "orb" but again no support for CC, you'd have to use an decoder)
You could also build a computer and put windows Media Center or mythTV on it. Then you could record shows, (closed captioning works most of the time) and then download them via FTP or telnet or something, and watch them on your computer.
There are also ways to download bootleg copies of movies and sometimes even TV shows but they'll never be closed captioned, don't even bother, and that is illegal, no legal way around that.
good luck