Unfortunately, when it comes to ponies, most of the shippings tend to be "yuri" (or lesbian)which isn't all too unexpected in a show with mostly female characters. Nothing against homosexuals here, I just don't see any of the ponies as lesbians (not even Rainbow Dash). So yeah: most of my favorite shippings will be heterosexual (what few actually exist in the fandom).
And I'm starting with my all-time favorite: Fluttershy/Big Macintosh (FlutterMac). These two were meant for each other. One's a shy girl; the other, a man of few words. And both are kind, gentle souls. They complement each other so well, which is why they're probably one of the most popular pony ships out there (not to mention the cutest). Besides, Fluttershy deserves a big, strong colt like Big Macintosh: strong enough to protect her, gentle enough to care for her.
Here's some of my favorite FlutterMac fan art:
Doesn't this picture just warm your heart? Make you want to give a little "dawwwww!" Simple, yet lovely.
Just the two acting cute together. Love how Fluttershy has flowers and butterflies woven into her hairand somehow, Big Mac has some in his hair too. It really suits herand Mac, too (both are into nature, after all).
The two running into each other as filies, presumably during the flashback in "Call of the Cutie." It would be nice if these two were smitten with each other as kiddies. Nothing like young love. Cute kids. Cute romance.
Big Macintosh offering Fluttershy a flower from the tree. What else can you say to this but "dawwwww!"
The two getting really close. Don't worry folks, I'm suring they're just cuddling and kissing. (Or are they?)
Remember in "Zero Lesson" when Twilight Sparkle went crazy and cast an attraction spell on her Smarty Pants doll? In this comic, Fluttershy asks Twilight to cast it on her in order to attract Big Mac. Though, if the comic were to remain true to the episode, Fluttershy should have the entire town chasing after her. But I like the outcome in this comic nevertheless. (Though she didn't really need a love spell for Big Mac, in my opinion. She's attractive just the way she is!)
And here's the outcome of the last comic. Don't worry, I think they're just sleeping together. (Or were they?)
This little comic is based off a fanfic by WarrenHutch called "Windfall," where Fluttershy gives birth to her and Big Mac's baby Windfall. This scene follows the aftermath, as the two parents cuddle together with their newborn. I think this selection from the fic sums up this scene nicely:
"The little bundle was the color and texture of a rosy peach, with a pair of impossibly delicate, downy wings folded against the curve of her back. These stretched out and refolded themselves as the foal squirmed in her father's lap and rolled over with a yawn followed by a tiny whisper of a sigh, revealing a sweetly sleeping face with even rosier cheeks and a wisp of silky pink mane falling across the filly's untroubled forehead.
At this feather light stirring, Big Macintosh's lower lip and chin started to tremble, a look of such profound love etched upon his normally impassive features that it was clear for all to see that not even the Princess's who moved Equestria's very sun and moon could ever hope to dislodge his tiny daughter from her seat on the throne of the giant earth pony's heart."
There are plenty of human pics of FlutterMac, but this has to be my favorite thus far. I don't know. In other pics, Fluttershy looks great, but I often don't care about how Big Mac looks. This one has a great human Fluttershy and Big Mac. Reminds me of the first image above.
Here's an image from the famous johnjoseco and his tumblr account Love Tommorow Love. Human Fluttershy and Big Mac are on a double date with Rarity and Spike (Another couple I adore).
Another picture from johnjoseco of human Fluttershy and Big Mac cuddling together in bed. Nothing explicit, but it is suggestive ("I'm the world champ, you know!"), so I'm labeling it as NSFW. Click above at your own discretion.
Yet another picture I'm labeling NSFW. Again, nothing explicit, but it is suggestive. Let's just say it involves Fluttershy in her undies being hid by Big Mac as Apple Jack enters the barn. What were they doing? You decide! Click above at your own discretion.