Anything from ShakespeareHemmingway. The guy, probably intentionally, writes some of the best so-bad-it's-good fanfic out there, usually starring Garfield (yes, that Garfield) as, well, practically Duke Nukem on steroids. But the thing that really makes it worth a read is that, unlike the usual troll-fic, this one is actually not laden with horrible grammar but instead uses an incredibly peculiar and consistent sentence-structure that somehow makes the entire thing even more hilarious.
For example, he always uses a person's full name and each line of his dialog is followed by a descriptive attribution, e.g.: "You are scum! - Jon Arbuckle declared with declaration."
Albeit somewhat tiresome, all of his works are absolutely hilarious.
But if we are about non-ironically good fanfic, I would recommend the first third or so of Harry Potter and the Methods of Rationality. It is a "what if?" scenario where Aunt Petunia managed to convince Lily to brew her a beauty potion, which turned her entire life around to the point where she eventually married an university professor instead of Vernon Dursley, so in this universe Harry grew up to be a prodigious rationalist and humanist in a loving household... and then the letter from Hogwarts shows up and hilarity ensues.
The fic does a pretty good job at deconstructing the magicalness of the Harry Potter universe without being overly malicious and all the while being absolutely hilarious. Sadly as the fic goes on it slowly becomes more and more detached from the HP universe and introduces a lot of author appeal elements, like introducing Ender's Game style wargames or slowly twisting the story into a soapbox for his "overcoming mortality" agenda, such as when it turns out that the Potter family has been researching immortality, or when Harry kills a Dementor by realizing that a Dementor is supposed to represent death (which is untrue by Rowling's admission, btw) and thus Harry being the first one to overcome death, and so on and so forth.
The first part of the story is still a great read, both thought-provoking and funny, you just have to be able to recognize the point at which it becomes a silly author-tract and leave it there.