Elizabeth II

Elizabeth II became the Queen of United Kingdom of Great Britain and Northern Ireland and various other countries in 1952.

20th century
The Wire attempted to take the energy from the millions of Humans watching her 1953 coronation on their televisions. However, the Doctor foiled the Wire's plans. (DW: The Idiot's Lantern)

In 1988, her path almost crossed that of the Doctor (who did not recognize her) at Windsor Castle. (DW: Silver Nemesis)

In 1997, Queen Elizabeth was deposed by Lord Xznaal in May, but was later restored to the throne and her Recoronation was held on 23rd November. (NA: The Dying Days)

21st century
In 2001, Dr. Who, a fictional duplicate of the Doctor, tried several times to assassinate her, convinced she was the leader of an oppressive regime. During an appearance in Sheffield he eventually succeeded, but the self-doubts of his accomplice Jason, coupled with his own essentially fictional nature, meant that the Queen survived after all. (NA: Head Games)

On Christmas Day, blood control powers of the Sycorax (operating out of a ship hovering over London) threatened to make Elizabeth II jump off a roof and kill herself, along with the rest of the British royal family. (DW: The Christmas Invasion) After the Battle of Canary Wharf (DW: Doomsday), the Queen ordered the immediate closure of Torchwood 1 (torchwood.org.uk). The Following "Christmas Star" incident (DW: The Runaway Bride) the following year, also in London citizens evacuated London when the next Christmas came around. The Queen, however, staunchly decided to remain in Buckingham Palace. When the Starship Titanic would have hit the palace on a collision course, but for the Doctor's piloting skills, she waved and thanked him by name. (DW: Voyage of the Damned)

Other references
The regime of a fascist parallel England had the British royal family executed. Presumably, this would have included Queen Elizabeth. (DW: Inferno)

The Doctor theorized that the royal family including Elizabeth II were Werewolves after Queen Victoria was attacked by one. (DW: Tooth and Claw)

Elizabeth II and Doctor Who
Elizabeth II reportedly enjoyed viewing classic Doctor Who and, when she met members of the Radiophonic Workshop commented on their connection with the series. The British press has reported that she now watches the new series.

Elizabeth II on Doctor Who
Mary Reynolds, uncredited, played the Queen in Silver Nemesis. Jessica Martin portrayed her in Voyage of the Damned. Archival footage of the Queen's coronation appeared in The Idiot's Lantern.

Behind the Scenes
An actor playing Elizabeth appeared in a comedy sketch with Catherine Tate.