Chima from Big Brother 11 was nicknamed "Hirochima" after her explosion(s).
Julie Chen has been nicknamed "Chenbot". House guests have actually called her "Chenbot" a few times, and CBS even has videos of Big Brother up on YouTube with "Chenbot" in the keywords, so they're well aware of this.
The origin of the nickname "Chenbot" is because Julie Chen has been able to say certain lines (mostly "but first") in the exact same way each time, even making the same movements as she looks towards the camera or stands up from a bench. You can see a Montage from season 6.
Gretel Killeen was named Gretski by housemate Blair in season one, and continued to be called Gretski by fans for the remainder of her hosting stint.
Victoria from BB 16 has been called Queen Victoria. Other people occasionally call her anything but her actual name, like Velma, Vacuum or Vuvuzela.
Internet Counterattack: The strongly negative reaction from live feed viewers during BB15, caused by the heavy amounts of racism, misogyny, et al by certain members of the BB15 cast provoked the broadcast show into addressing it on air.
Team America (US 16) had to do something that would impress America. They (mostly Frankie) decide to perform a play (actually the contestants doing a series of imitations of other players) instead of using it to save Donny, the most popular contestant of the season. When it came for America to vote on whether they reserved to win money for their play, the answer was an "overwhelming no."
Romance on the Set: Being in a house with nothing but the same people again and again can made sparks fly
Lisa and Eric in Season 3, though it did not last long
Eric and Jesicca in Season 8, though they have now broken up
Nick with Daniele and Jen in Season 8, in the show and after the show respectively.
Jeff and Jordan in Season 11
Brendan and Rachel in Season 12, they tied the knot during 2012
Danielle and Dominic in Season 13, they tied the knot during 2013, to the surprise of many.
Chantelle and Preston in Celebrity Big Brother 4, who were wed just months after the season and divorced 10 months later. which resulted in a rather awkward reunion when they met each other again in Ultamite Big Brother.
Jon and Neda (Season 2) are revealed to be dating after their season ended.
In BB5 US, Nakomis and Cowboy's father was initially chosen for casting, which he declined. During the interview, he revealed that both of them never knew their existence, thus the second part of the DNA twist is born.
In BB6 US, Ivette's girlfriend was intended to be her partner, but was replaced with her friend, Beau.
Also, Dick and Daniele (both from BB8) made it to the finals in BB6 casting, but was not chosen.
In BB7 US, Bunky, Dana, Ivette, Lisa, Michael "Cowboy", and Monica were candidates to come back into the house, but lost both the public vote & the producer's vote.
In BB 8 US, Jessica's nemesis was originally a rival from a dance team.
In BB 11 US, Jessica (BB 8, Popular), Micheal "Cowboy" (BB 5, Offbeats) and Brian (BB 10, Brains) are candidates to come back into the house, but their cliques lost the HOH competition to Jessie (BB 10, Brawns)
In BB 12 US, a fourteenth houseguest named Paola had been cast, but left during sequester and was not replaced.
In BB 13 US, a cast video of someone named "Jason" was actually filmed but for some reason, he was dropped during sequester.
In BB 14 US, an early trailer showing some contestants showed someone named Mike but for some reason, was replaced with Joe for reasons unexplained. One Steve Limit , maybe?
Also, Rachel from BB12 and BB13 US was supposed to be one of the coaches, but as she declined to become married, Britney replaced her.
Why Fandom Can't Have Nice Things: Thanks to people making huge efforts to slant the game in their favour in the first season, they put in limitations on how the audience can affect the game. In particular, people have botted the site so that Ronnie and later Jeff or Jordan would get the Coup de'Tat in season 11. CBS put in restrictions on how many votes can go, and then later on randomized the positions on the site so that if you clicked the same place twice, you wouldn't click on the same houseguest you clicked on previously. In the recent America's Vote, you have to have an account with the site and can only vote ten times.