There's a couple. I'm gonna include some spoilers here for people who might want to watch a certain show or be watching it now.

I'd have to say imo one of the saddest is in The Wire

It's not exactly sad, but probably the most moving moment for me in TV history is the episode of The Simpsons where Homer quits his job to work at the bowling alley & has to beg for his job back when Maggie is born. Mr Burns takes him into a room with a big plaque saying 'DON'T FORGET YOU'RE HERE FOREVER'. The original point was that there were no pictures of Maggie & Homer says he keeps them where he needs them most & it cuts to the same room full of pictures of Maggie covering the plaque's wording to say 'DO IT FOR HER'. The Simpsons has a few that can get me thinking about it as does Futurama.