The "started before 1988" criterion eliminates two no-brainers, both of which debuted in 1988 ("The Kids in the Hall" and "The Wonder Years").
The first reply in the thread covers many of the shows I'd have listed (my tastes align with 75-80%, so I won't relist)
I still watch Star Trek: TNG semi-regularly, and M*A*S*H when I'm in the mood.
I'll add...
--The Facts of Life (the first four or five seasons, before they moved the girls out of the school setting -- especially liked the first season with the large cast)
--Kids of Degrassi Street (this show is like taking a time machine back to my childhood -- all filmed in real settings and used amateur child actors...reminds me of growing up in the era)
--Degrassi Jr. High (and Degrassi High, even though it's 90s)
--as a kid: Mr. Dressup (Casey and Finnegan era) and The Friendly Giant