Barney's big speech in the end of Barney in Concert. He talks about how having such good friends is like having a big family. Awwwww.
In "Waiting for Santa", after the Backyard Gang reaches Santa's workshop, Derek rushes to remove his coat and helps Tina with hers.
The song Friends Are Forever. This song is sung by Michael and Amy's mother and the song is about how friendships will last forever, when they're make-believe. This is a heartwarming/tearjerker song because it portrays the almost sad idea that a friend might and will eventually leave. That's why imagination and pretend is so important because your make-believe friends will last forever.
Derek and Michael spend a whole episode arguing over who gets to keep a picture they made together. They bury the hatchet, and give it to Tosha.
When she doesn't know what to give Barney for his birthday, Kathy offers him her teddy. He gently declines the gift, telling Kathy that while presents are nice, she already gave Barney the best gift of all: "the gift of love."
My Family's Right For Me. The entire episode.
The season finale has Barney sharing a gift that will always show him and his friends someone special. It's a mirror.
This exchange, from "The Alphabet Zoo":
Shawn: Jason, can you teach us how to say something else by signing? Jason: Sure, and here's one that's easy to do, and you can say it to very special friends, like Barney. * Signs "I love you, Barney" and gives him a hug* Barney: Aw! *signing* Thank you, Jason. Shawn: What did you say, Jason? Jason: I said,*signing* "I love you, Barney."
"What's in a Name?" Even though Chip is obviously concerned that he will miss his baseball game, he offers to help her to learn all of the letters in her name.
Linda: Thank you, Barney. And thanks, Chip, for helping me today. Chip: Hey, what are big brothers for?
As they leave, the look on Chip's face says "I am so proud of her", and the look on Linda's face says "I have the greatest big brother in the world!"
Barney's Great Adventure
Cody admitting that Barney's a pretty cool guy in the end
Michael: We think you're a Super Dee Duper friend to all of us, too, Barney. Linda: That's right! Michael: From the oldest... Linda: ...To the youngest! All Present (except Barney): You can always count on us!
It helps that it leads into You Can Count on Me, this time being sung by everyone except Barney (He sung it earlier).
Kathy (as a teen) and Linda's duet of Me and My Teddy (known to be Kathy's trademark song) in the same video. It was like a passing of the Moe torch.