Star Wars

Star Wars was a film series, the American premiere of the first part of which the Doctor and Frobisher attended at Mann's Chinese Theatre in 1977. The Doctor claimed to prefer the Special Editions and noticed that Peter Cushing who had played Grand Moff Tarkin looked familiar. (PDA: Mission: Impractical)

Minor references

Returned to her old haunts in Perivale, Ace learned from Ange that their mutual friend Flo married a "brain-dead plumber" they had nicknamed Darth Vader. (DW: Survival)
Sam Jones had Star Wars toys as a child. (EDA: Alien Bodies)
The Doctor told Martha Jones that Jar Jar Binks' clan were "...good people...very hospitable." (TDA: Forever Autumn)
Both Mr Grantham and Clyde Langer made reference to the series, the latter comparing himself to Luke Smith's mentor, like Obi-Wan Kenobi. (SJA: Warriors of Kudlak)

Clyde may have meant this as a humorous reference to Luke's first name.

At the end of a holographic communication left to Jack Harkness, another Time Agent, John Hart mockingly re-created the "Help me, Obi-Wan Kenobi, you're my only hope" line from the first film. (TW: Kiss Kiss, Bang Bang)

Peter Cushing, of course, had played both Dr. Who and Grand Moff Tarkin.
The duel on the Sycorax asteroid in The Christmas Invasion may take some cues the duel between Darth Vader and Luke Skywalker in The Empire Strikes Back. In both scenes, the hero (the Doctor in this case) loses a hand and the weapon holding it. Later, the destruction of the Sycorax asteroid by the Jathaa weaponry is similar to the Death Star's destruction of Alderaan in A New Hope.
Star Wars creator, George Lucas is an avid fan of the original Doctor Who series.
Actor Harrison Ford (Han Solo) was offered the role of the Eighth Doctor in the 1986 Doctor Who television movie but turned it down rather than have a television commitment tie him down. (At the time, the movie's producers hoped to make it the pilot for a re-launched Doctor Who series.)