Our House was a show that I distinctly remember watching a lot when I was young, even though it didn't last long. It had Shannen Doherty, Chad Allen, Deidre Hall and Wilford Brimley as the grandpa. The mother had to bring her kids to live with her father-in-law, so it was all sorts of touching and sweet to see a family be a family. I even liked their basset hound.
80s and 90s TV show honorable mention: One Day at a Time (a darn fine show.)