He usually did not engage in computer-like literal thinking, though on one occasion he followed Romana's instructions to "forget it" to the letter and erased all knowledge of tennis from his memory banks. (TV: The Stones of Blood) In another he took Romana's exclamation "Blast it!" as a command, and fired his blaster. (TV: Shada, WC: Shada, AUDIO: Shada, PROSE: Shada). Despite this, he occasionally showed a sense of humour, jokingly answering the question "What do you eat?" with "Ball bearings" (AUDIO: The Beast of Kravenos).
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)
Although the first incarnation of K9 does not appear again in televised Doctor Who media, he is the star of the 2009 K9 television series, in which he undergoes a sort of "regeneration" process from which a new, more sophisticated and futuristic K9 emerges; in the first series of K9, the character is transported to London c. 2050 by Professor Gryffen (Robert Moloney). Though on regeneration the character loses his memory of his adventures with the Doctor, he assists Gryffen and several teenage companions against a dystopian regime of "The Department". The upgraded K9 has new specifications, sporting a sophisticated head-up display, the ability to fly, and more powerful laser weapons.