This one is from the Fresh Prince of Bel Air. I honestly almost cried watching this once. Basically, Will's Dad split when Will was just a kid and has recently tried to get back into Will's life. They decide to go on long trip together (Will's dad is a trucker) but his Dad cancels the trip at the last second and attempts to run out on Will all over again. Here is the last scene from that episode (you have to follow the link):
Sorry for just posting a link but youtube wouldn't let me embed this one. This is like one of 4 serious/emotional moments I can remember even happening on the show (the others being Phil's heart attack, Carlton taking speed he got out of Will's locker, and Will getting shot.) It has always been one of my favorite moments in tv history because for one I love this show and still watch it when it reruns, and also because I think Will Smith nails the delivery. Makes me even more thankful for my own Father, who has always been everything for me.