Fan Convention

Rupert: Hobbits will be mustering under Gandalf as usual in the Ops Room. Esoterica with the Master Mage is in a dimension yet to be fixed... Filking will be in Home Universe this year... ...Stan, who are these people?
Stan: Ordinary people having fun, I expect.

—Deep Secret

Also called just Convention or Con (or, pre-WWII, "fan meeting"), the Fan Convention is where fans of a particular work or medium all meet together, discuss their show(s) and ask questions of the stars. A number turn up in costume. The tone of fan conventions varies; some are relatively quiet get-togethers where the focus is on talking about things in the fandom, some are essentially trade shows, some are excuses to party all weekend, most are a combination of all three of these.

Frequently parodied in the case of a Show Within a Show, where in(s)ane questions to stars are common. The Trope Codifier for these parodies is from a December 1986 episode of Saturday Night Live with William Shatner - the famous "Get a life" sketch.

The largest fan convention in the world is Comiket, the twice-annual doujinshi show in Tokyo. Other famous cons include the World Science Fiction Convention (or "Worldcon", the second-oldest extant SF fan convention - they decide who gets the Hugo Awards each year), the San Diego Comic-Con (originally covering Comic Books, but has grown to also cover comic-book-related media such as superhero films) and Gen Con (the largest Tabletop Games convention in North America).

The Other Wiki has a set of pages about fan conventions, starting logically enough with their "Fan convention" page.

No real life examples, please; The Other Wiki does a better job of listing these than we could ever hope to do. Feel free to add "Fan Convention" as a category to any fan convention page here, though.

Examples of Fan Conventions include:

Anime and Manga

Comiket and its Bland-Name Products has a separate page.

Drama Con takes place at the fictional "Yatta!con".

Comic Books

In the Sandman series, a hotel puts on just such a convention...for serial killers.

Fan Works

From Yu-Gi-Oh!: The Abridged Series:

Florence: I activate Dark Sanctuary! Now the duel will take place in a twisted and horror-filled environment where only the bravest souls dare to venture.
Yami Yugi: An anime convention?

At one point in The Secret Return of Alex Mack, Alex and Willow attend San Diego Comic-Con, where in addition to enjoying the convention and taking part in cosplay, Alex makes an appearance in her superhero identity, Terawatt (to judge a contest of Terawatt cosplayers!) while Willow disguises herself as Alex in cosplay to help support Alex's secret identity.

Film

Galaxy Quest had a major, mostly affectionate, parody of this.
The documentary Trekkies touched on the subject.
The Bag Witch Project, a Blair Witch parody short film by Toxic Bag Productions, tells the sorry tale of three attendees at GenCon, who get hopelessly lost in the hallways of the Milwaukee convention center.

Literature

Sharyn McCrumb's novel Bimbos of the Death Sun sets a murder mystery at a con, where a popular but volatile author is murdered while writing his latest novel.
Most of the Diana Wynne Jones book Deep Secret takes place at a sci-fi/fantasy convention. Of course, there are real wizards there.
The Dresden Files novel Proven Guilty takes place in part at a horror movie convention.
Night of The Living Trekkies is a book about a zombie outbreak at a Star Trek convention; there is a trailer for the book here.
Lost at the Con is about a Gonzo Journalist sent to cover Griffin*Con, a thinly-veiled Expy of DragonCon. As very much a not-geek, his articles (which punctuate the act breaks) start out being very disparaging of the fans, the guests and the con itself, but eventually he winds up defending them against the kind of Jerk Jocks who pick on people that just want to have fun and be themselves.

Live-Action TV

One episode of CSI involved a Furry convention.
- Vanity Fair and MTV also had hilariously misinformed "documentaries" on the Furry fandom, complete with supposed explorations into a furry convention.
- Conventions and CSI seem to go well together; aside from the Furry Convention, they also had episodes involving a convention for midgets and one for large people.
- And one for Astro Quest, the Fictional Counterpart to Star Trek.
Doctor Who has a fair number of these, with the Outpost Gallifrey "Gallifrey One" conventions being fairly well known. Peter Davison turned up to a few in his Fifth Doctor costume, before deciding that since others were doing it, it was a bit odd and stopping. Of course, Patrick Troughton famously died at such a convention.
The episode "The Real Ghostbusters" of Supernatural has Sam and Dean attending a convention for fans of the novel series based on their lives, which most fans assume is fiction. Hilarity Ensues.

Video Games

In Metal Gear Solid, Dr. Hal "Otacon" Emmerich's nickname comes from the real-life Otakon convention.

Web Comics

Narbonic inspired both fictional and real-life examples.
- Within the comic, Dave Davenport travels to Dave-Con, the annual convention of the Dave Conspiracy (every member wearing a badge that reads, "Hello, my name is DAVE").
- In Real Life, the readers of the comic organized Narbonicon, an annual event celebrating the comic and its author, Shaenon Garrity. It was held during the six years of the comic's original run, but discontinued once the "Director's Cut" version (*cough*reruns*cough*) began.
El Goonish Shive had a non-canon side story that took place at San Diego Comic-Con.
The first Umlaut House comic had Evil Con, for mad scientists.
Insecticomics includes several instances of characters (actually, the author cosplaying) attending the real-life BotCon.

Web Original

That Guy With The Glasses runs into a convention in pursuit of Casper the Friendly Ghost, during the Nostalgia Critic's review of the movie Casper. Variously-costumed conventiongoers help him with the chase.
- Chester A. Bum and 90s Kid attend Youmacon once, where Chester discusses yaoi with a Chester cosplayer, 90s Kid has a 'Dude-off' with a 90s Kid cosplayer, and they interact with other con-goers.
- In a later video, Chester and Lester A. Bum gather con-goers at Daisho Con 2010 to re-enact Harry Potter and the Deathly Hallows - Part 1.

"RUN! AAAAAAAA!"

Western Animation

In an American Dad episode, the Villain of the Week is hiding in a convention, and the only way to get to him is using Steve´s proficiency in elven language.
Freakazoid! chased Caveman and was chased by Fanboy during a convention.
- The Caveguy episode was notable, as Freakazoid talks to the fans in lieu of his creator, and scares Caveguy off by speaking Klingon to him
- In an earlier episode, while trying to escape from Fanboy (who was trying to become his sidekick), Freakazoid fell into a sci-fi convention. He then finally got Fanboy off his back by pointing out Mark Hamill and tempting Fanboy with the more glamourous prospect of Jedi Knighthood.
The Simpsons had Homer saving Mark Hamill from psychotic fans.
The battle in Robot Chicken between Star Trek and Star Wars fans at a scifi convention.
Phineas and Ferb has an episode set at a "Sci-Fi and Fantasy Convention," with Phineas being a Sci-Fi fan, Ferb being a Fantasy fan, and Candace being an Otaku for cutesy Japanese character Ducky Momo. The Sci-Fi and Fantasy sides actually get into a war, until Phineas and Ferb come up with a plan to remind them that that they're all nerds there, and that Hate Dumb is stupid.