Barf and Belch

Barf and Belch (a.k.a Barfbelch) is the Hideous Zippleback of Ruffnut and Tuffnut. Barf and Belch are like their owners, they have trouble which head goes what direction and focusing on one target. However, unlike Ruffnut and Tuffnut, they can work to together and find their owners annoying with their constant bickering.

In the film
At the climax of the film Ruffnut and Tuffnut, along with the rest of Hiccup's friends, were taught to ride dragons to beat the Red Death. Ruffnut and Tuffnut ride a Zippleback.

In Riders of Berk
It was revealed in the show that the left head's name is Barf and the right is Belch, with Ruffnut apparently commanding Barf while Tuffnut controls Belch.

In the episode In Dragons We Trust, Barf and Belch are framed by Mildew of the crime of stealing all the boots of the village during "boot night," sleeping in a bed of boots. They are then proven innocent by the comparison of their tracks and the tracks at the scene, noting how their tracks are deeper.

In Twinsanity, Barf and Belch briefly went rogue after Ruffnut and Tuffnut's conflict with each other reached a point where they were issuing contradictory orders to the head they controlled, the Zippleback roaming around the village just as renegade Viking chief Dagur the Deranged arrived to discuss a treaty. Wishing to sign the treaty in dragon's blood, Dagger captured and nearly decapitated Barf and Belch, but the twins were able to reconcile in time to help their dragon escape, the other dragons faking an attack on the training ring to conceal Berk's new trained dragons in order to avoid provoking war.

Trivia

 * Barf and Belch were originally supposed to be ridden by Fishlegs; he briefly rode on Belch in Twinsanity after the dragon flew away without the twins, but shared this role with Snotlout as Snotlout rode on Barf.
 * As of Defiant One, Barf and Belch are the only dragons in the Dragon Academy whose gender has not been specified; Toothless, Hookfang and Thornado are all male- or at least generally assumed to be male-, while Stormfly and Meatlug are female.