John Rimmer was the eldest brother of Arnold Rimmer and a high flying officer in the Space Corps. He stole Arnold's first girlfriend when a 17-year-old Arnold brought her home to meet the family on Io for the first time; Arnold discovered them together in the greenhouse. (Novel Better Than Life)
There were 4 Rimmer brothers: John, Howard, Frank and Arnold. Their father was obsessed with getting them into the space corps and continually tested and cajoled his sons to that end. To ensure they met the height requirements, Mr. Rimmer used a traction table to stretch his sons (RD: Better Than Life).
The three older brothers bullied Arnold fiercely, although he saw it as playful high jinks. Even when they placed a landmine in his sandpit, he laughed it off. During their "Three Musketeers" game, Arnold always had to play the Queen of Spain (RD: Polymorph).
Behind the scenes
John was played by an unnamed child actor in "Polymorph".
In a deleted scene from "Rimmerworld", Kryten revealed that all 3 of Arnold's brothers became highly decorated officers, but all went insane and in some way killed their crews. Arnold was rather touchy on the subject.
In the booklet accompanying the DVD of Series III, it was suggested that John and his brothers were actually the sons of the man they called Uncle Frank. Either way, they would actually be Arnold's half-brothers, as it is revealed in "The Beginning" that his real father was the family gardener "Dungo" Dennis.