As old as they look Twilight Zone was such a great show, great writing, excellent actors and, good B&W production. Throw in The Outer Limits (the old ones). Meantime, since I understand that it's never NOT been on since 1951 when it started, I would need a TV somewhere in the house always playing I Love Lucy. I can veg out on almost any really dumb 1960's sitcom, especially Gilligan's Island and I Dream of Genie.
The Muppet Show is also important, as is The X-Files, Miami Vice and some sort of compendium of Saturday Night Live shows. Cheers should be there too, as should 30 Rock.