Fluttershy's explanation for why she follows Rainbow Dash:
Rainbow Dash…um, well she makes you believe: in her and in yourself. She can stand up and announce that she’s going to do something dangerous, impossible and even a little, um, crazy and you believe that she can really do it. She’s not one of those ponies who brags about doing great things that they’ve never done—she goes out and does it. Even when you think she’s being irresponsible and impossible, you want her to succeed, against the odds. And then she does it and it makes you believe that you can do the impossible too. But it’s not what she represents that I became friends with. I became friends with her. I know she puts up a bold front, but she is one of the most steadfast and brave friends ever. Rainbow Dash would never let a pony down when they really needed her. She’s held me up for so long and never deserted me. I heard somepony say that when strong ponies fall—the kind who’ve held you up for so long—they fall harder under the weight they’ve been carrying for us. That’s why I’m here for her.
Applejack offers Rainbow her home while she's in Ponyville, recognizing that Rainbow was running away from home. She only just met her that day.
Twilight explains the source of her Shrinking Violet nature, tearfully recounting how her entrance exam to Celestia's academy ended with her magic running completely out of control, transforming her parents and turning a baby dragon into a giant. Unlike the canon universe, where Celestia intervenes and restores Twilight's confidence, Twilight's magic runs rampant until she exhausts herself. She's accepted into the academy, because the testers fear that untrained, Twilight is danger. Traumatized, Twilight notices her Cutie Mark and assumes her special talent is a potential for destruction. This haunts her until she meets Rainbow Dash and Applejack, who convince her that her Cutie Mark means a talent for magic, not destruction. Rainbow explains how she earned her Cutie Mark after she accidentally (and unbeknownst to her) knocked Fluttershy off her cloud to the ground below. Applejack got her Cutie Mark after she returned from Manehattan after leaving her family. They tell Twilight that their Cutie Marks don't represent indifference to their friends' danger or abandoning one's family, but rather a love for flight and a dedication to one's family, and that she shouldn't view her Cutie Mark as a emblem of her past mistakes. Twilight's relief has to be read to be fully experienced, and Twilight finally starts to come out of her shell, forging bonds of friendship with Rainbow and Applejack.
In May The Best Friends Win, after Twilight exposes Trixie for the self-serving Jerkass that she is to Rainbow Dash, she still urges Dash to try to make peace with her. Twilight knows what it's like to have no friends and doesn't wish that on any pony, even one like Trixie.
And when this leads Dash to offer Trixie a Last-Second Chance to apologize for the damage she's done and possibly rebuild their friendship, Trixie swallows her pride and accepts.
After Rainbow's confrontation with Celestia about her actions and behavior over Nightmare Moon's return, Ditzy comforts the saddened princess and helps her realize just what she is to Rainbow, and what she means to her (subsequently helping them reconcile):
(concerning Rainbow Dash) You never held her when she was scared or felt panic rising up inside you when she went missing or got hurt? Whenever she was sad you never felt like you would move the sun just to make her day a little brighter? You never felt your tummy feel like ice when she was doing something dangerous or felt a pit in your stomach when she was mad at you? You take care of her when she’s sick or hurt, comfort her when she needs it, take pride in her accomplishments, feel sad when she’s sad, happy when she’s happy. You say you aren’t a mom…but you try to be a good role model for all ponies. You set rules, try to teach them right from wrong, how to think for themselves, discipline them when they do something wrong. If you ask me, you are a mom…just on a bigger scale. And if you’re like a mom for all of Equestria, then you DEFINITELY are a mom to Rainbow Dash in particular.
Rainbow Dash's and Dinky's scene at the beginning of Hot Heads, Cold Hearts, and Nerves of Steel is heart-melting wonderful.
And then there's their reunion after Dinky escapes from Sombra's forces.
Rainbow Dash, Shining Armor, and Cadance repairing their friendships, banishing Sombra's Windigos in the process.
The foals being reunited with their families.
"Rainbow Triumphant": Rainbow Dash's forfeiting the Best Young Fliers competition in order to prevent it from becoming the Rainbow Dash show, preserve its nature as a venue for up-and-coming fliers to show their stuff, and help the other contestants regain their confidence. She gives a heartfelt speech about the importance of the competition in inspiring others to strive to be the best, and explains that she doesn't want to ruin that. This despite the fact that she feels like she's letting her friends and family down by forfeiting.