In the Doctor Who continuum, the Time Lord known as the Doctor often brings others along on his various adventures across time and space. Due to the Doctor's well-documented interest in humans, the vast majority of his companions have been human or descended from humans. However, he has been known to bring non-humans as well, even choosing machines as companions on occasion, such as K-9, who was not only a long-time companion of the Fourth Doctor, but eventually played key roles in two of the show's spin-offs.
Susan Foreman - the earliest of the Doctor's companions, Susan was known as the Doctor's granddaughter, a distinction that has greatly confused the fanbase since the Doctor's children have never been seen or heard from. In response, a large number of fanfictions and semi-official Expanded Universe stories have claimed that Susan and the Doctor were never biologically related. However, since the Ninth Doctor alluded to having been a father at one point, it is possible that Susan was simply descended from the Doctor in the typical sense.
Barbara Wright and Ian Chesterton - the Doctor's first known human companions, dating back from the era when Doctor Who was intended as an edutainment show rather than the science-fiction adventure that it later became. They were written out of the show after their characters used hijacked Dalek technology to travel back to 1965.
Jamie MacCrimmon - a companion of the Second Doctor native to 18th century Scotland, Jamie had one of the longest continuous runs of any companion, appearing in more episodes than even several later Doctors would. When the Time Lords sentenced the Third Doctor to life on Earth, large portions of Jamie's memory were wiped, and he was sent back to his native time period.
Sarah Jane Smith - a companion of the Third and Fourth Doctors, Sarah Jane went on several pivotal adventures with the Doctor before his TARDIS dropped her back on Earth to answer a summons to Gallifrey. She was very popular during her run, and remained popular enough even decades later that she was brought back during the Tenth Doctor's run, and later received her own spin-off.
Rose Tyler - the first companion of the revived series, Rose Tyler was created as a foil for the Ninth Doctor, who was much more disparaging toward humanity than his predecessors. She remained as the first companion of the Tenth Doctor when the Ninth Doctor regenerated after his first season, and is often shipped with one or both of the two Doctors she spent time with by fans. Rose was left in an alternate universe after helping to thwart a dual invasion of Daleks and Cybermen, and traveled back and forth between that universe and her native one for several seasons, finally staying in the alternate universe after helping the Doctor and several of his other former companions thwart yet another Dalek attack.
Jack Harkness - While Jack Harkness, or "Captain Jack", only appeared in a few episodes as the companion of the Ninth Doctor and an ally of the Tenth, he was so popular among the fans and writers that he became a main character on another spin-off, Torchwood.
The position of companion to the Doctor has proved to be irresistible to Sues and Stus, often self-inserts, who will slander the existing companions or simply supplant them to diminish their role in the story, allowing the OC to steal the spotlight. Occasionally, the Doctor is even seen to be travelling alone when he enounters the Suvian, his previous companions having vanished into a plothole to allow the new arrival to obtain the coveted position of sole companion. In rare cases, the companions will even be killed off to allow the OC to take their place. If the Doctor is seen to be generally unaffected by the death of the companion, or get over the death rather quickly, he is drastically OOC at such a level that an agent may need to see if he has been replaced.
This distortion of canonical events is often coupled with the way the Suvians introduce themselves; while the Doctor's methods of choosing a companion may vary between incarnations, the companion-Sue will often introduce herself at random and impress the Doctor without doing anything, which is OOC for any one of his forms.