Ask Pipsqueak has at least one or two moments that can make even the most hardened cynic go "D'awwww!". Its run by PashaPup, who's responsible for quite a few of the entries in the Fan Art section.
From Carrot Top's Garden is this mini-story  about Dinky, Ditzy, Carrot Top, Noi, and Sparkler and the Sisterhooves Social. Especially the "can I have a sister?" part, Dinky and Sparkler bonding, and Ditzy telling Sparkler as far as she's concerned, she's as good as a daughter to her.
From the same place it takes the "Derpy eating Carrot Top's food" concept and give it a tear jerking and heartwarming twist
Ask Echo the Wonderbolt, a recently established Tumblr for a blind OC Stand In pony (she appeared in a brief Off Modelshot in "The Best Night Ever") who uses echo-location to navigate. The fact that she's also a Wonderbolt injects a shot of awesomeness.
She was actually given the canon name Fleetfoot in the show a few days after the blog started in "Sweet and Elite". Considering Fleetfoot won the race, it makes Echo's reaction all the more sweet.
Stop asking Twilight which one of her friends is her favorite. From "Ask Twilight Sparkle Anything." Part 1 and Part 2.
Pretty much any of the Master's Pet the Dog moments with Pinkamena. In fact, the same could be said for the reverse. Their wholerelationship has a very Love Redeems-ish feel to it, given that it's basically the one positive trait exhibited by either pony.
The finale to Fire Starter Spitfire, especially the end, where the world goes from the black and orange/yellow palette that the blog had been since the beginning to normal colors, indicating that Spitfire has finally made peace with her inner demons and is able to move on with her life.
That story line gives THREE different blogs major heartwarming moments. Aside from the Discorded Whooves overcoming his own corruption for a while, Miss Twilight Sparkle is given the opportunity to raise a foal, giving her a ray of hope hope in the grimdark Ponyville she lives in, and Pregnant Scootaloo winds up gaining a mother of her own.
Twilight: You're a silly pony if you think you needed to say 'I wish' for one of those.
The story behind the creation of Rainbow-less Dash, which can be read here. An outcast girl with odd hair, a guy that wanted to be her friend, and a shared love of a simple television show leading to a shared love between them...
Hazel reading a comatose Trixie her favorite bedtime story in Ask Stalker Trixie. if you look closely, you'll see that Trixie, despite her coma, is smiling as Hazel reads to her.
This post from an Ask-Cheese Sandwich blog (if you're a Cheesepie shipper).
Even Murdershy has it's moments like the (now sadly unlinkable) moment after it had just changed art-style and a asker had insulted fluttershy's new body as 'ranchy', over a hundred followers sent in comments to reassure her that her she was still beautiful(just in a more fan-servicey way).
Ask Twixie Genies is just full of these, but one standout is this little gem. Genie!Twilight cheering Genie!Trixie up when a poster asks about the latter's lonliness is just adorable. "Without a doubt", indeed...
Despite Twilight pulling quite a few trollish antics on Trixie due to viewers' wishes, becoming an immortal Reality Warperhasn't clouded her morals in the least. In the second comic linked above, Twilight is very disturbed when an anonymous poster suggests using her newfound powers to "get rid of" the Changelings as payback for her brother's wedding.