A fan fave (also: fan favo[u]rite) is usually a character, work or someone from cast & crew that becomes popular within a fandom without no apparent reason or even despite (for example for antagonists).
In cases of characters, fan faves are usually not main characters.
The popularity of a favorite is not just measured by the number of openly declared fans, or the number of related fanworks, but rather in the feelings of devotion and affection they give/received off in their fans. So many faves can be callouted problematics by some non-fans or antis.
Examples
Cast
Examples Wanted : Editors are encouraged to add more examples or a wider variety of examples.
Character
Pendrell , Alex Krycek , the Lone Gunmen , Mr. Chuckleteeth, writer Darin Morgan and director Kim Manners in The X-Files
Alice Jones in Once Upon a Time
Judar , a character in the manga series Magi
Ella Lopez in the Lucifer TV series
Lex Luthor in the Smallville TV series
Jadzia Dax in Star Trek: Deep Space Nine
Eric Effiong in Sex Education
Eliot Waugh in The Magicians
Sarah Jane Smith in Doctor Who
Castiel and Charlie Bradbury in Supernatural
Nikolai Lantsov and Wylan van Eck in the Grishaverse
Mercy in Overwatch
Tara Maclay in Buffy The Vampire Slayer
Clint Barton in the Marvel Cinematic Universe
Guerrero in Human Target
Nathan Summers and Domino from Deadpool
Martin Fitzgerald in Without a Trace
Cayde-6 , a Non-Playable Character in the Destiny video game
Figwit , a background elf in the Lord of the Rings films
Teresa Moreno , a Spanish guerrilla in the Sharpe Fandom
Solas in Dragon Age: Inquisition
Stanley “Grunkle Stan” Pines in Gravity Falls
Alex Kamal in The Expanse
Mistress, Ivan the Apprentice, Sandoval the Xoan Ambassador, the Snow Queen, and Greir the Lesbian Mercenary in the Oglaf webcomics
Damian from The Bright Sessions
Cara Mason in Legend of the Seeker
The Captain a character from the BBC sitcom Ghosts
Nick Fury and Phil Coulson from Captain Marvel
Delirium from The Sandman comics
Venom and Eddie Brock characters by Marvel
Noah from Total Drama
Fan Fictions
Examples Wanted : Editors are encouraged to add more examples or a wider variety of examples.
Fan Vids
Examples Wanted : Editors are encouraged to add more examples or a wider variety of examples.
Gaming
Examples Wanted : Editors are encouraged to add more examples or a wider variety of examples.
Pairings
Examples Wanted : Editors are encouraged to add more examples or a wider variety of examples.