With his great intelligence, he had a tendency to bore people with facts and did not stop immediately when asked, as he did to Leela on Pluto. When being told that he would have to stay behind in the TARDIS, K9 often argued, giving the Doctor reasons why he should go such as "he would be a good dog." K9 always wanted to assist the Doctor. He had great intelligence and skill at chess, claiming to be able to beat the Doctor in six moves (although this may only have been because he was programmed with all chess games since 1886). (TV: The Sun Makers, The Androids of Tara) K9 had an aggression mode. (TV: State of Decay)
Damaged by the time winds, K9 Mark II could not cross back into N-Space with the Doctor. He decided to stay behind at the Gateway with Romana II to help her free the remaining Tharils from slavery. (TV: Warriors' Gate) Eventually, Romana II and the presumably repaired K9 returned to their own universe and K9 Mark II came to live on Gallifrey. (PROSE: Lungbarrow, WC: Shada, AUDIO: Zagreus)
When being imprisoned by the Sporraxx they tried to access K9's memory core. Memories that K9 had assumed to be erased were slowly coming back and the Sporraxx got to know more and more about K9's past. They reprogrammed K9 to protect a small spherical marauder bomb, that would destroy Earth. However K9 was able to break free of their control, because deep in his memories a sense of right and wrong prevailed. He took the bomb back into the Sporraxx space ship where it exploded. (COMIC: Short Circuit)
When the Tenth Doctor created K9 Mark IV to replace K9 Mark III, he added a shiny metallic blue paint job and other improvements, including an omniflexible hyperlink facility. (TV: School Reunion) Later, though, K9 reverted to his old dark green colour. (TV: Invasion of the Bane) In battling Mr Smith (and following the battle) K9 displayed a teleport facility and a laser weapon similar to the previous K9s'. (TV: The Lost Boy)
Introduced into the plot in The Invasion of Time, K9 Mark II first actually appear on-screen in The Ribos Operation (1978). More mobile than his predecessor, Mark II exhibited the ability to sense and warn others of danger. He travels as a companion alongside the Doctor and Romana. Around the time of Romana's regeneration (the transition from actress Mary Tamm to Lalla Ward), the K9 character was explained as suffering from "laryngitis" to accommodate Leeson's departure from the series at the start of the 1979–80 season; for this time, he was portrayed by David Brierley, until Leeson's return for the 1980–81 season. When the Doctor and Romana travel to the parallel universe of E-Space, K9 is severely damaged, in Warriors' Gate (1981). The damage was such that K9 could only function in E-Space; when Romana decided to stay and forge her own path, the Doctor gave K9 to her. The character makes subsequent appearances in remakes of the unfinished serial Shada, alongside the Eighth Doctor (Paul McGann); the 2003 Shada audio play and webcast depict K9 Mark II as having returned to Gallifrey with Romana, now Lady President of the Time Lords, where the Doctor visits them. It is not clear if either of these audio appearances are considered canonical in relation to the continuity of the TV series.