So you want to name your fandom. It's a natural urge: Fandoms are about communal identity, and there's nothing more communal than sharing a name. There are a few standard conventions to follow or flout, as the case may be.
Examples: Beliebers, Gleeks, Twihards, Fanilows, and X-Philes (Justin Bieber, Glee, Twilight, Barry Manilow, and The X-Files, respectively)
When to Use: This only works if the title or name of the object of your affection sounds like a word commonly associated with the concept of affiliation.
Suggestions: Do Devo fans really not call themselves Devotees or the Devoted? That is a missed opportunity! Psy fans can be Dipsyples, Cee-Lo fans can be Ceelots, Justified fans can be Justifiers, and Joe Biden fans can be Abiders.
Examples: Dead Heads, Parrotheads, Dunderheads, and Rent-Heads. (The Greatful Dead, Jimmy Buffett, The Office, and Rent.)
When to Use: Widely applicable! Head on, apply directly to your fandom.
Suggestions: Arrowheads, for fans of the new CW show Arrow; Lemonheads, for fans of 30 Rock; Subheads, for journalists and for fans of Last Resort.
Riffs on Titles
Examples: Trekkies, Truebies, and Whovians. (Star Trek, True Blood, and Doctor Who.)
When to Use: Seems to be reserved for things in the fantasy/sci-fi/mythical vein, but that needn't be so.
Suggestions: The Vampire Diaries fans could be Diarists, fans of the game Minecraft (they're still out there, right?) could be Miners (or Crafters). Supernatural fans already sometimes go by Super Freaks, but Supesters ("SOOP-sters") seems like more fun.
Riffs on Names or Nicknames
Examples: Whedonites revere Joss Whedon, teammates on Team Breezy revere Chris Brown, teammates on Team Coco revere Conan O'Brien, members of the KISS Army revere KISS, those buzzing in the Bey Hive revere Beyoncé, and Colbert Nation revers the Comedy Central host.
When to Use: Clarity is key! "Whedonite" isn't catchy per se, but it's unambiguous and memorable.
Suggestions: Poehlerbears for Amy Poehler fans, Weinermobiles for Matt Weiner fans.
Examples: Little Monsters (Lady Gaga fans), Juggalos and Juggalettes (Insane Clown Posse Fans), Nerdfighters (Vlogbrothers fans).
When to Use: "Juggalo" is vaguely derived from the word "juggler," "Nerdfighter" from a misread of the title "Aero fighter," and "Little Monsters" appears to be plucked from the ether. You can't control for serendipity!
Suggestions: Alas, it doesn't work like that. These kind of arbitrary names either stick or they don't.