Using various search criteria to try to locate a complete list of TV shows, I think I may have found such a thing. If you know of better sources please link to them.
So far, I believe Category:American television series by decade is going to suit my own purposes for locating every show I have ever seen!
As bonus material with more specific breakdowns, refer to Category:American television series
I had an early edition of this book ~30 years ago, back before the explosion of cable and first-run syndication, and it seemed to be pretty exhaustive (it included stuff like the Dumont network, local shows of historic note, daytime shows and soap operas, early first-run syndication, etc.). I can’t comment on the current edition, but if it has kept up the same breadth of coverage it should be a good resource.
Oh man I used to pore over that book as a kid! It was my Wikipedia!
It’s still around. I have the 9th edition. It boasts having more than 6,500 series and is 1,832 pages long. The only drawback is in it’s title: it only features prime-time series, so it makes no mention of stuff like Oprah or the Today Show.
TV Guide. It’s been around since 1953. After 2000, it went downhill, though. I dug out my special collector’s covers set of The Simpsons, Issue #2482, from Oct. 21-27, 2000. In addition to commentary on 24 characters in The Simpsons, there was sports news, celebrity updates, an interview of a reality TV contestant, an article about Tim Russert, news about the 2000 election (remember that?) and letters. That’s 70 pages. That’s not what makes TV Guide comprehensive.
What makes TV Guide comprehensive is the 182 pages listing every show of each day of the week. For example, it shows that at 8:30 AM on Saturday, October 21, 2000, you could have watched One Saturday Morning on ABC for 2 hours, Adventures of Tintin on channel 9, Pokemon on channel 20, Angela Andaconda on Fox Family, Making the Video on MTV, Rocket Power on Nickelodeon, or watch for 2 hours and 15 minutes, Mutiny on the Bounty, a four-star movie on TCM.
I was watching Pokemon. 
Ok. That’s about 2500 issues. 2500 weeks. Nearly 50 years of complete, documented, listings of broadcast TV and cable TV.