Hoo boy.... I definitely can't say what I consider to be the "best" fanfic I've read, but I can point out some contenders for the title - stories that had an impact on me, all of them because of great storytelling, and because they managed to touch me in some way.
The Only Tree in the Forest by Hap: I guess you could describe it as a historical chronicle of sorts, from the perspective of a single character as they watch the world change around them. It becomes obvious which tree fairly early in the story, but that's not something the story hinges on. One downside, in my opinion, is that it ends rather abruptly.
Package Not Delivered by M48 Patton: A short, somewhat bittersweet story about mailing ponies, and a rather poignant take on some of the events of the first season.
Fahreneigh 451 by Liquid Truth: I'll admit it right now, I'm a huge sucker for Bradbury, so when a story successfully emulates both his style and puts a unique-yet-familiar spin on the source material, that easily goes in my top ten percentile of things I like by default. Sad and surreal, it's one of the favourite stories I've ever read.
80 Days 'Til the World's Farthest Shore by Cynewulf: It's hard for me to pinpoint why exactly I like this story so much - possibly because of the optimism inherent in it, when it touches on the inevitabilities of Twilight's immortality, and where it goes from there. For what is essentially a short adventure novel, it's actually rather action-free, but that works in its favour, as it gives focus to the protagonist's own insights and thoughts. I also admired certain... parallels, though some of them will probably be missed on the first read.
Mythic Dawn by MagnetBolt: Frankly, if there's a single story I've read that would qualify as a perfect sequel to FiM, this would easily be it. It follows some of the show's formula - in fact, it jumps into it with an unabashed sense of humor - but it quickly hits its own beat while staying true to MLP's message.
The Eternal by Forestfire34720: MLP fanfiction has had its share of "after the end" stories, and this is one of them. And yet, while the story focuses on a sad event - the passing of a dragon - it's a happy tale, not because of what has happened, but what is happening. In the words of Robert Frost, "In three words I can sum up everything I've learned about life: it goes on."
Amber Ashes by GMBlackjack: This is one of those "adventure epic" stories, and it deserves that title in spades. It's a Mane Six story of sorts, although it leans heavily into the alternate universe angle, and while it certainly has the whole "save the world" thing going on, that's only one aspect of many plots and subplots that take place. It's funny, it's dark, it's dramatic, it's amazing, it's ridiculous and scary and, well, I could go on. It's quite a long read, clocking in at almost 100K words, although that's just a drop in the bucket compared to the source material. If you're looking for a novel to read, you can't go wrong with this.
And finally, I can't omit Friendship is Optimal by Iceman. Hoo boy. One of the earlier works of the MLP fandom, it inspired of its own canon, though far from the scope of works like Past Sins or Fallout: Equestria. One could argue it's not really a MLP fanfic or just a science fiction story, given that it takes place in the real world and there are no real ponies or the Magical Land of Equestria to speak of, but in either case, it's one hell of a ride from the beginning to end. What you take away from it is probably going to vary heavily - from happy, to bittersweet or, in my case, being literal nightmare fuel. But whatever the case, it's a sobering idea that I can only hope will remain fictional.