On Doctor Who, Donna Noble is a companion to the Doctor. She was portrayed by veteran comedienne Catherine Tate. She was the companion to the Tenth Doctor, portrayed by David Tennant.
Donna Noble has an interesting history in Doctor Who. She is first seen in the closing moments of Series 2, as a teaser for her appearance in the special The Runaway Bride. After that, she wasn't seen for a series, before being brought back as the regular companion for series 4, and then having a role in the final special of Tennant's run, The End of Time.
Externally to the show, the role also is an interesting one. Catherine Tate was already well known to the viewing public in the UK for her eponymous sketch comedy show. For her to become a co-star on Doctor Who would be somewhat like if Tracey Ullman or Tina Fey were given a lead role in Star Trek. (Although one famous comedienne did have a recurring role in Star Trek). And this made a big difference in how the character was presented in the show.
The traditional role of a companion on Doctor Who is to be a straight man to The Doctor, performing the role of audience surrogate and average person to the eccentric, alien, confusing and sometimes grandiose Doctor. The Tenth Doctor, as portrayed by David Tennant, definitely is one of the more hammy of The Doctor's incarnation. But with Catherine Tate, the producers found an actress with enough comedic talent to turn The Doctor into the straight man. The interplay between the two actors was great, allowing some lines and scenes to come alive that I can't imagine any other pair to do. Two scenes, in Partners in Crime and The Unicorn and the Wasp, where the two frenetically mime to each other, seem almost like improv scenes. One of them, at least, actually was.
Other than providing comedy, Donna was also a humanizing force on The Doctor, taking him to task for his occasional callousness much more than his two previous companions could. Donna herself begin as somewhat of an air-headed, banal person, but upon meeting and traveling with the Doctor, she became more and more intelligent and resourceful.
Although the end of Donna Noble's traveling with The Doctor was in large part based on the external reality that companions, and the actors that portray them, are cycled through Doctor Who regularly, it was still an especially final parting. Some think it was even cruel and (of course) misogynist, and it is one of many situations in Doctor Who that still cause consternation amongst the fans.