8. Smith And Jones
In the first Martha Jones episode, the hospital Martha (Freema Agyeman) works at is transported to the moon, where the Judoon invade in search of a fugitive alien known as a Plasmavore. The Plasmavore is vampire-like, and can disguise itself as the species whose blood it drinks. The Judoon can only find the Plasmavore by scanning for and finding alien DNA, which causes a few entertaining moments with the Doctor, since he is an alien as well and doesn't wish to be detected.
When He Should Have Regenerated: At one point, the Plasmavore drains the Doctor's blood to the point of him passing out. Later, Martha is able to restart the Doctor's two hearts by giving him CPR. If there has been enough blood loss that the Doctor's hearts can't keep him alive, then CPR certainly wouldn't have revived him. Martha, as a medical student, should have known better. There is a very plausible chance that the Plasmavore didn't drink enough of the Doctor's blood to kill him. However, if this was the case and he had only fallen unconscious, Martha wouldn't have had to give him CPR as she did. Again, a medical student would know better.