There are a few that I would rank up there, from various different canons (good fanfiction to me is like potato chips: you cannot have just one). Most of them will be from various versions of Batman, mainly because I find that is one of those rare fandoms where fans actually know the canon and its characters, and have their heads on their shoulders when it comes to writing.
Serious Stories:
A Light in the Tower. This is pretty much a prequel to
The Nightmare Before Christmas, and focuses on Sally, her life as a new, learning creation, her relationship with Dr. Finklestein, and eventually her love for Jack. Unfortunately, it has not been updated in forever. (Curse you, Silver Lady. -_- Finish it!) Definitely one of the better
Nightmare fanfics you will
ever find.
Throwaway Card. I have to re-read this one (I honestly
cannot remember the plot), but I do remember it was one of the best Joker fanfics I have
ever stumbled upon.
Someone to Scream for Me.
Van Helsing. It is told in Verona's point of view, and focuses on Dracula's Brides, and their view on family.
From the Desk of Severus Snape. I understand the formatting is off on this one (wall of text and all). This was written long before
Order of the Phoenix came out (and in a way, I think it still sort of can fit into the established canon), so for its time, I consider it a good, simple piece of work.
Noctis Timeo. Vampires in Gotham, basically. This is proof that vampire stories
can still be done right, and I liked that while the vampires
were a big part of the plot, they did
not take all the spotlight. I also liked the character development in both the vampires and the starring canon characters.
Funny Stories:
Just Another Arkham Experiment. Basically, the inmates of Arkham have to spend a day in each other's shoes. One of several amusing tales from a Fanfiction.net writer named Serb. Honestly, just about
anything in the
Batman: The Animated Series universe by Serb is guaranteed to amuse you.
Another one by the same author that I really enjoyed was
The Bargain, which is a Scarecrow/Poison Ivy pairing that, in my opinion, was written in a way that
could realistically work. While I do not ship the said pairing (I like the "married to his work" Scarecrow better), I do like how the author put thought and effort into thinking about how such a pairing would work, and carefully crafted the relationship while keeping the characters and their personalities in mind. There were a few moments I
would consider a bit out-of-character, but for the most part, it was an enjoyable read because of the effort and thought so clearly put into it.
I am the Master of Fear. I will be honest that this is my own story. It is a
Batman: The Animated Series and
The Nightmare Before Christmas crossover, which sprung from a thought of having the Master of Fear (the Scarecrow) and the Master of Fright (Jack Skellington) eventually meeting.
Tripping Arkham Asylum. Basically what happens when Arkham inmates are taken on a field trip to an aquarium. Hilarity
does honestly ensue.