This has happened on this very wiki! (not repeatedly, though): after TV Tropes was mentioned in XKCD, a mob of newbies washed over the forums and wiki, trashing the servers.
Through the nature of Wiki Walking, TV Tropes itself has a tendency to give support to Youtube videos that illustrate a certain trope. These videos would otherwise probably fall into the yt obscurity, and thus you may see a top comment saying "Who else got here from TV Tropes?"
Naughty Tentacles and The Second Google Incident killed Porn Tropes and led to the creation of a new organization of Tropers dedicated to screening new and existing pages for adult content. If a page was lucky, it came back locked. If not, it was hit with a salted nuke. Also, the creation of new porn-related pages is today considered by This Very Wiki to be our equivalent of a capital offense. As far as tropes go, Naughty Tentacles in particular is to blame for that.
Newbie Boom: This wiki gets a Newbie Boom each time an outside community links in. xkcd linked here once and killed the server for part of a day.
Old Shame: Many longtime tropers are ashamed of the former Troper Tales and Fetish Fuel sections of the site, and for good reason. The entries there were so... uh, off-color, giving wayToo Much Information about the tropers who posted there, that they damn near dragged this site's reputation down to the level of 4chan. Thankfully, it was removed and will never come back. The two sections are now hosted on separate sites.
This wiki has a Rule of Cautious Editing Judgment meant to prevent any Flame Wars (read that page for more). Unfortunately in some situations, some tropers completely ignore this rule, leading to the mods locking the page most likely for good, which means nobody gets to add and edit future tropes. A few pages have also been locked to stop persistent vandals who are too savvy to be simply blocked. On a related note, the YMMV tropes and pages were created to keep the more controversial tropes off of the main pages, but even that has led to YMMV pages ending up getting locked or even deleted.
In extreme cases, there's the Permanent Red Link Club, in which the tropes are so misused, become a magnet for racial slurs and personal attacks, and the like that not only the page is locked, the page (and in some occasions, the entire trope) gets deleted, never to be used again. Forever.
The trope Please Elaborate was meant to be a handy tool for tropers. If one found a poor example, but didn't know the source material well enough to expand it themselves, they would add that example to Please Elaborate, and a troper with actual knowledge of said example could fix it. It joined the Permanent Red Link Club when lazy tropers started adding Please Elaborate to their examples pre-emptively to pawn off the actual elaboration of said example to other tropers.
And in less extreme but still unfortunate cases, Real Life examples can be cut and prohibited from a page if things get controversial enough. On that note, there's also the Example Sectionectomy, for which examples are either cut entirely or relegated to a separate area such as Darth Wiki or the Discussion tab if things get nasty.
This wiki used to have a "strikethrough markup", but it was eventually disabled as people were using it simply to sneak in Take Thats and such. Texts that were previously striked are now hidden texts. The strike format is still usable in the forums, though.
Colored text was removed due to negative use and abuse of hard-to-read colors. Now even the easy-to-read colors like red and blue are forever gone from the site. It was eventually restored for the forums.
The Archive of Bellicose Lexicon Entities was a series of articles listing tropers accordingly to their visions on trope naming, images, example lists and the like. However, since it was determined that these articles, rather than serving their purpose as fun places for like-minded tropers to associate, were inspiring antagonism and factionalism among our user base, they have been discontinued and all of them eventually redirect back to that index. Tropers are no longer listed, as they can simply add themselves through their userpages anyway.
Trolls, vandals and sockpuppeteers attacking the site and its articles led to a recreation of the login/handle creation system in spring, replacing the standard sign up theme with a CAPTCHA approval add on.
For similar reasons, troper pages can now only be edited by the tropers themselves who created them. The days when a good-faith user could sign or leave a fun commentary in another troper's page (which was known as "fun vandalism"), or even simply fix a spelling mistake, are unfortunately over because of this.
Many threads in the forums that contained intelligent discussions get locked when people start and keep trolling, flaming each other, or derailing the topic after being told more than once by the moderators to knock it off, ruining it for everyone else who wished to continue the discussion in a civil manner. While some threads get temporarily locked to let everyone cool off, other threads can get locked forever, never to be reopened unless a mod says otherwise.
Zero Context Examples used to be a free pass back when many trope names were self explanatory until people started throwing in tropes on list of works without giving any examples at all, not realizing that people won't always get why a character is or is not a Knight Templar or that readers may not want to look up every single trope if no examples are present. Nowadays, tropes listed in works that have no examples are usually edited to be hidden until someone can find actual examples that fit the listed trope.