Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Tear Jerker: The Cosby Show
"It seems like just yesterday I was holding my baby in my arms. And today my baby had two babies. Now she's a mother..."
One-shot character Ray Palamino, played by Sammy Davis Jr., introducing himself to his pregnant granddaughter who he hadn't seen in over 20 years.
"Hey everybody! My name is Ray Palamino. I'm 67 years old... and I can't read." As much as the character claims that it doesn't bother him, the strain in Sammy Davis Jr's voice completely contradicts it.
Also Clair's speech to Theo why she's so proud of him graduating from college in the final episode.
Going back to season 2, there's the letter that Cliff and Clair read to Denise after she announces her college decision.
A positive example: Cliff's friend Jake and Jake's friend Ernest finally resolving a feud they'd had between each other for decades after learning their children were getting married to each other and were prepared to have the wedding without their fathers present if it became necessary.
A Meta example: The final episode aired during the 1992 Los Angeles race riots. Cosby went on air earlier that day begging people in the city to stop what they were doing.