The Other Wiki. To quote the article over there, calling something fancruft is implying that "it is of importance only to a small population of enthusiastic fans of the subject in question." Over there, this usually takes the form of adding minor details about fictional works to entries to which they only mildly apply (under the heading "In Fiction" or "In Popular Culture"). The name comes from cruft, which is computer geek slang for "garbage."
Most of what would be called fancruft in The Other Wiki would feel right at home in this wiki — we call it "examples" and we like it; successfully qualifying for "fancruft" here requires some really high-quality, genuine brand of narrow-minded devotion. Unfortunately, that's of ample supply on the internet. It's one of those things that is hard to define but immediately jumps at you when you see it. You know you've encountered fancruft when reading a paragraph, you suddenly get a distinct picture of some very excited person typing in the edit box with fervor, going all "Oooh! My niche! I get to popularize my niche! My niche my niche mynichemynichemyniche!!!"
This takes many forms. Rambling on the All Psychology Is Freudian page about some non-funny, non-relevant in-joke that used to be mildly popular in the Yahoo! Geocities professional yo-yo forum a contributor moderated circa 2001. Two-paragraph long rants on why opinions differ as to whether the invocation of Not Allowed to Grow Up in Pokémon implicitly lends credence to some secret preteen attraction between Ash and Gary. Square Peg, Round Trope. Renegade Entry Pimping. It's seldom good news.
Of course, this is all in theory. In practice, one man's expansive and entertaining divergence is another's fancruft, and there's no objective magical way to tell them apart. "I don't care for this" is not, in and of itself, a reason to delete anything; chances are pretty decent that someone else does care (at the very least, the person who added it). If you're looking to improve a well-meaning yet out-of-place contribution courtesy some over-eager niche enthusiast, just treat the symptoms and the problem is likely to go away. Trim Walls of Text, cut Conversation in the Main Page, rewrite the example to focus on actual tropes as employed in the actual work as opposed to Audience Reactions. Only delete it as a last resort.
When in doubt, err on the side of accepting it as a legitimate, interesting contribution. Ultimately we're all fans, and this wiki is our great big fancruft compendium. For the time being, there's enough server for everyone, so don't push for the sake of pushing.